We have the expression:
[tex]\frac{(p+q)^2}{p-2q}[/tex]We have to evaluate it for p = 4 and q = 8.
To do that, we replace the variables p and q with the given values and calculate:
[tex]\begin{gathered} f(p,q)=_{}\frac{(p+q)^2}{p-2q} \\ f(4,8)=\frac{(4+8)^2}{4-2\cdot8} \\ f(4,8)=\frac{12^2}{4-16} \\ f(4,8)=\frac{144}{-12} \\ f(4,8)=-12 \end{gathered}[/tex]Answer: The value of the expression when p = 4 and q = 8 is -12 [Second option]
John is listing each step of the equation +4 = 10 – 3 폼 5+4= 10 - 3 *5 = +4= 7 c+4= -35 TE -39 What was his mistake?
Answer:
x+ 4= -35
Explanation:
Given the equation:
[tex]\frac{x}{-5}+4=10-3[/tex]The next step is:
[tex]\frac{x}{-5}+4=7[/tex]The next step should have been:
[tex]\begin{gathered} \frac{x}{-5}=7-4 \\ \frac{x}{-5}=3 \end{gathered}[/tex]Therefore, his mistake was the step below:
[tex]x+4=-35[/tex]A high school has 52 players on the football team. The summary of the players weight is given in the box plot approximately what is the percentage of players weighing less than or equal to 194 pounds
Explanation
We are given the box plot below:
We are required to determine the percentage of players weighing less than or equal to 194 pounds.
We know that a box plot interprets as follows:
Therefore, we have:
[tex]Q_1=194[/tex]Also, we know that:
[tex]Q_1=\frac{1}{4}\text{ }of\text{ }100\%=25\%[/tex]Hence, the percentage of players weighing less than or equal to 194 pounds is:
[tex]\begin{equation*} 25\% \end{equation*}[/tex]-4x - 3 = -11x + 16
We want to find which value must have x, so this equation is true:
-4x - 3 = -11x + 16
In order to solve the equation for x, we want to "leave it alone" on one side of the equation.
In order to do that we just have to remember one simple rule:
Finding xStep 1- taking all the terms with x to one side
We are going to take all the terms with x to the left side:
-4x - 3 = -11x + 16
↓ adding 11x both sides
11 x - 4x - 3 = 11x -11x + 16
↓ since 11x - 4x = 7x (left) and 11x - 11x = 0 (right)
7x - 3 = 0 + 16
7x - 3 = 16
Step 2- taking all the numbers to the other side
7x - 3 =16
↓ adding 3 both sides
7x - 3 + 3 = 16 + 3
↓ since -3 + 3 = 0 (left) and 16 + 3 = 19 (right)
7x + 0 = 19
7x = 19
Step 3- leaving x alone on the left side
7x = 19
↓ dividing 7 both sides
7x/7 = 19/7
↓ since 7x/7 = x (left) and 19/7 ≅ 2.7
x ≅ 2.7
Answer: x = 19/7 ≅ 2.7
Hello,Can you help me with the question in the photo?Thank you,
Answer:
4, 12, 44, and 173.
Explanation:
Given the recursion formula:
[tex]\begin{gathered} a_n=4a_{n-1}-4 \\ a_1=4,n\geqslant2 \end{gathered}[/tex]We want to find the first four terms of the sequence.
[tex]\begin{gathered} a_2=4a_{2-1}-4=4a_1-4=4(4)-4=16-4=12 \\ \implies a_2=12 \end{gathered}[/tex]Similarly:
[tex]\begin{gathered} a_3=4a_{3-1}-4=4a_2-4=4(12)-4=48-4=44 \\ \implies a_3=44 \end{gathered}[/tex]Finally:
[tex]\begin{gathered} a_4=4a_{4-1}-4=4a_3-4=4(44)-4=176-4=173 \\ \implies a_4=173 \end{gathered}[/tex]The first four terms of the sequence are 4, 12, 44, and 173.
f(x)=x^2+2x+4Evaluate f(x+5).Simplify the answer
We have a function:
[tex]f(x)=x^2+2x+4[/tex]We have to evaluate f(x+5).
To do so, we replace the argument x from the definition of f(x) with "x+5":
[tex]f(x+5)=(x+5)^2+2(x+5)+4[/tex]Now, we can expand this and simplify as:
[tex]\begin{gathered} f(x+5)=(x+5)^2+2(x+5)+4 \\ f(x+5)=(x^2+2\cdot5x+5^2)+(2x+10)+4 \\ f(x+5)=x^2+10x+25+2x+10+4 \\ f(x+5)=x^2+12x+39 \end{gathered}[/tex]Answer: f(x+5) = x² + 12x +39
С.c7. The difference of two positive numbers is six. Their product is 223 less than the sum of their squares. Whatethe two numbers?
Let two unknow positive number is "x" and "y"
Difference of two positive number is 6 that mean:
[tex]x-y=6[/tex]Their product is 223 less than the sum of their square:
[tex]\begin{gathered} x\times y=x^2+y^2-223 \\ xy=x^2+y^2-223 \end{gathered}[/tex]Substitute x with variable y:
So,
[tex]\begin{gathered} x-y=6 \\ x=6+y \end{gathered}[/tex]Put the value of "x" in another equation:
[tex]\begin{gathered} xy=x^2+y^2-223 \\ (6+y)y=(6+y)^2+y^2-223 \\ 6y+y^2=36+y^2+12y+y^2-223 \\ y^2+6y-187=0 \\ y^2+17y-11y-187=0 \\ y(y+17)-11(y+17)=0 \\ (y+17)(y-11)=0 \\ y=-17;y=11 \end{gathered}[/tex]Given number is positive that mean y=11 and so value of x is:
[tex]\begin{gathered} x=6+y \\ x=6+11 \\ x=17 \end{gathered}[/tex]So the number is 11 and 17.
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!
The measure of ∠B AND ∠H is ∠B = 58° and ∠H = 122°
What is parallel lines?
Parallel lines are coplanar, straight lines in geometry that don't cross at any point. When two planes in the same three-dimensional space are parallel, they never cross. Curves that maintain a set minimum distance from one another and do not touch or intersect are said to be parallel curves.
If parallel lines are cut by a transversal , then corresponding angles are equal in measure.
∴ ∠B≅∠F
∠A≅∠E
∠C≅∠G
∠D≅∠H
If parallel lines are cut by a transversal , then interior angles on the same side are supplementary.
∠C+∠E=180°
∠D+∠F=180°
If one of the angles ( let it be ∠E) formed measures 122°, then m∠C=180°-122°=58°.
m∠B=m∠C=m∠F=m∠G=58°;
m∠A=m∠D=m∠E=m∠H=122°.
To learn more about parallel lines from the given link
https://brainly.com/question/11848535
#SPJ1
Answer:
if angle a measures122 degrees than angle b measures 58 degrees and angle h measures 122 degrees.
Q: what are parallel lines and their angles?
Answer:
Two lines that are stretched into infinity and still never intersect are called coplanar lines and are said to be parallel lines. The symbol for "parallel to" is //.
There are 4 types of angles formed between parallel lines i.e Corresponding angles, alternate angles , Interior angles, adjacent angle
the project is #Spj4
Step-by-step explanation:
What is the approximate Probability of drawing a spade Card from a standard deck of shuffled cards?Group of answer choices1/21/41/5212/52
Given,
The number of cards in a standard deck is 52.
Required:
The probability of drawing of spade card.
The number of spade card in deck is 13.
Consider,
A is the event of drawing of spade card.
Probability is calculated as:
[tex]Probability\text{ =}\frac{Number\text{ of favourable events}}{Total\text{ events}}[/tex]Substituting the values then,
[tex]\begin{gathered} P(A)\text{=}\frac{N(A)}{Total\text{ events}} \\ =\frac{13}{52} \\ =\frac{1}{4} \end{gathered}[/tex]Hence, the probability is 1/4.
-47 > 1 - 8x ≥ -63????
Answer:
6<x<8
Step-by-step explanation:
−47>−8x+1>−63 (Simplify all parts of the inequality)
−47+−1>−8x+1+−1>−63+−1 (Add -1 to all parts)
−48>−8x>−64
−48/−8 > −8x/−8 > −64/−8 (Divide all parts by -8)
and the answer would be: 6<x<8
What is the slope of the linear function given the following table?
х у-3. 6 -2. 51/3-1. 42/30. 43. 2Help please !
Let's use two points of the table:
[tex]\begin{gathered} (x1,y1)=(-1,3) \\ (x2,y2)=(0,1) \end{gathered}[/tex]Let's find the slope using the following formula:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{1-3}{0-(-1)}=-\frac{2}{1}=-2[/tex]Using the point-slope equation:
[tex]\begin{gathered} y-y1=m(x-x1) \\ y-3=-2(x+1) \\ y-3=-2x-2 \\ y=-2x+1 \end{gathered}[/tex]-------------------------------------------------
For the 2nd table:
[tex]\begin{gathered} (x1,y1)=(-3,6) \\ (x2,y2)=(0,4) \end{gathered}[/tex]Let's find the slope:
[tex]m=\frac{4-6}{0-(-3)}=-\frac{2}{3}[/tex]Using the point-slope equation:
[tex]\begin{gathered} y-y1=m(x-x1) \\ y-6=-\frac{2}{3}(x+3) \\ y-6=-\frac{2}{3}x-2 \\ y=-\frac{2}{3}x+4 \end{gathered}[/tex]I purchased a subscription to Brainly, but I can't figure out how to use it. I've snapped pictures of the questions, I snapped pictures of the problems. neither works. I get no answers. I can't type in a problem with numerous exponents. I don't know what to do. Can you help?
Given the functions:
[tex]\begin{gathered} f(x)=3x^{\frac{1}{2}} \\ \\ g(x)=2x^{-\frac{1}{4}} \\ \\ h(x)=6x^{\frac{1}{4}}^{} \end{gathered}[/tex]Let's solve for h[f(g(x))].
To solve this function operation, let's solve in parts.
First step is to find f(g(x)).
We have:
[tex]undefined[/tex]Which of these expressions represents the product of an irrational number and a rational number being irrational?
ANSWER
Option B
EXPLANATION
We want to find which of the expressions is in the form:
Irrational number * Rational number = Irrational Number
An irrational number is a number that cannot be expressed as a ratio or fraction of two integers, such as pi or roots.
Options A and C cannot be correct because they each have two irrational numbers multiplying one another.
Simplifying Option D, we have:
[tex]\begin{gathered} 3\cdot\text{ }\sqrt[]{9} \\ \Rightarrow\text{ 3 }\cdot\text{ 3} \\ =\text{ 9 } \end{gathered}[/tex]The correct option is B, because:
[tex]\begin{gathered} \frac{1}{4}\cdot\text{ }\sqrt[]{44} \\ \frac{1}{4}\cdot\text{ }\sqrt[]{4\cdot\text{ 11}} \\ \frac{1}{4}\cdot\text{ 2 }\cdot\text{ }\sqrt[]{11} \\ \frac{1}{2}\sqrt[]{11} \end{gathered}[/tex]That is an irrational number that is a product of a rational number and an irrational number.
Therefore, the answer is Option B.
3The number of hours that the employees at the local Fry's grocery store worked last week is normallydistributed with a mean of 28 hours and a standard deviation of 4. What percentage of employees workedbetween 24 and 36 hours?Answer:
We can solve this question by using the fact that a normal distribution is symmetric and using the empirical rules. The empirical rules are
• 68% of the data falls within one standard deviation of the mean.
• 95% of the data falls within two standard deviations of the mean.
• 99.7% of the data falls within three standard deviations of the mean.
In our problem, the mean is 28 and the standard deviation is equal to 4. Our interval is 24(one standard deviation below the mean) and 36(2 standard deviations above the mean)
[tex](24,36)=(28-4,28+8)=(28-\sigma,28+2\sigma)[/tex]Our area is the area that falls within one standard deviation of the mean plus the area between one standard deviation and two on the positive side. The first area is 68% of the data, and the second area we can calculate using the fact that a bell curve is symmetric. Since 68% of data falls within one standard deviation and 95% of the data falls within two standard deviations of the mean, the difference between them represents the data that falls between one standard deviation and two standard deviation.
[tex]95-68=27[/tex]Since the distribution is symmetric, the data that falls between one standard deviation and two standard deviation on the positive side is half of this value.
[tex]\frac{27}{2}=13.5[/tex]Now, we just add this value to 68% and we're going to have our answer.
[tex]68+13.5=81.5[/tex]The percentage of employees worked between 24 and 36 hours is 81.5%.
A farmer fell asleep under a tree in his apple orchard while thinking about pie. While he was sleeping, a squirrel knocked an apple off a branch of the tree. The function f (d) = (see photo) can be used to find the amount of time in seconds that it takes for the apple to drop acertain distance d, where d is in meters.Step 1 of 3 : If the apple was connected to a branch that was 3 meters above the farmer's head, how long would it take before the applehit the top of the farmer's head? Round your answers to the nearest hundredth.
Solution
Step 1
Write the time function equation
[tex]f(d)\text{ = }\sqrt{\frac{2d}{9.8}}[/tex]Step 2
d = 3 meters
[tex]\begin{gathered} f(3)\text{ = }\sqrt{\frac{2\times3}{9.8}} \\ f(3)\text{ = 0.78 seconds} \end{gathered}[/tex]Final answer
0.78 seconds
Draw the image of the figure under thegiven transformation.5. 180° rotation6.reflection across the x-axis7. (X,y) - (x - 4, y + 1)8. reflection across the y-axis
To obtain the 180° rotation, obtain the (-x,-y) coordinates of the given (x,y) coordinates.
The given coordinates of the points are as follows.
[tex]A(3,0),B(1,4),C(5,3)[/tex]Thus, the new coordinates will be as follows.
[tex]A^{\prime}(-3,0),B^{\prime}(-1,-4),C^{\prime}(-5,-3)[/tex]Plot the coordinates in a Cartesian coordinate system and then connect the points.
Krystals a Jewelry business. At a craft market, she boys and sell the bracelets she makes each week The graph below shows her weekly profit from bracelet sales 20 What is the amount of profit, per bracelet?
To find the amount of profit per bracelet we need to find the slope of the line. The slope is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]To find this slope we need two points on the line (whichever points we like). From the graph we select the points
Professional athletes are some of the highest paid people in the world. The average major league baseball player's salary has climbed from $1,998,000 in 2000 to $2,866,500 in 2006
Answer:
[tex]L(y)=144750y+1998000[/tex]
The slope means that each year the average professional baseball player's salary increased by $144,750 for every year after 2000.
The y-intercept means that in year 0 (2000) the average professional baseball player's salary was $1,998,000
The predicted average salary in 2007 is $3,011,250
(b)
[tex]E(y)=1998000\cdot1.062^y[/tex]The initial value represents the average professional baseball player's salary in year 0 (2000), which was $1,998,000.
The growth factor means that the rate of change increases each year by 1.062 times the previous year's increase.
The predicted average salary in 2007 is $3,044,233.94
Explanation:
The problem gives us two pieces of information:
In year 2000, we call t = 0, the average salary was $1,998,000
In year 2006, we call t = 6, the average salary was $2,866,500
If we want to make a function of the average salary variation over the years, we have two points that must lie in the equation of that function:
(0, 1998000) and (6, 2866500)
For (a) we need to assume that is linear growth. The equation of a line is:
[tex]y=mx+b[/tex]Where:
m is the slope
b is the y-intercept. In this case, since we established the year 2000 as t = 0, b = 1998000
Given two points P and Q, we can find the slope by the formula:
[tex]\begin{gathered} \begin{cases}P=(x_P,y_P){} \\ Q=(x_Q,y_Q)\end{cases} \\ . \\ m=\frac{y_Q-y_P}{x_Q-x_P} \end{gathered}[/tex]Then, if we call:
P = (0, 1998000)
Q = (6, 2866500)
[tex]m=\frac{2866500-1998000}{6-0}=\frac{868500}{6}=144750[/tex]Thus, the equation of the linear growth model is:
[tex]L(t)=144750t+1998000[/tex]Now, we can use this to find a prediction for 2007. 2007 is 7 years since 2000; thus t = 7
[tex]L(7)=144750\cdot7+1998000=1013250+1998000=3011250[/tex]In (b) we assume an exponential growth. The formula for the exponential growth is:
[tex]y=a(1+r)^t[/tex]Where:
a is the initial value. In this case, the average salary in 2000, $1,998,000
r is the ratio of growth. We need to find this value
t is the time in years
Then, we can use the point (6, 2866500), and the fact that a = 1998000:
[tex]2866500=1998000(1+r)^6[/tex]And solve:
[tex]\begin{gathered} \frac{2866500}{199800}=(1+r)^6 \\ . \\ \sqrt[6]{\frac{637}{444}}=1+r \\ . \\ 1.062=1+r \end{gathered}[/tex]We call the term "1 + r" growth factor.
Now, we can write the formula:
[tex]E(t)=1998000\cdot1.062^t[/tex]To find a prediction of the average salary in 2007, we use the function and t = 7:
[tex]E(7)=1998000\cdot1.062^7=1998000\cdot1.5236=3044233.937[/tex]
which of these choices show a pair of equivalent expressions? Check all that apply. A. 5^2/3 and (sq rt. 5)^3 B. (4 sq rt. 81)^7 C. 7^ 5/7 and (sq rt. 7)^5 D. 6 ^7/2 and (sq rt. 6)^7
SOLUTIONS
Which of these expression shows a pair of equivalent expressions:
Option A is wrong:
[tex]\begin{gathered} 5^{\frac{2}{3}}=(\sqrt{5})^3 \\ \sqrt[3]{\sqrt{5})^2}=(\sqrt{5})^3 \end{gathered}[/tex][tex]\begin{gathered} \sqrt[4]{81)^7}=81^{\frac{7}{4}} \\ \sqrt[4]{81^7}=\sqrt[4]{81^7} \end{gathered}[/tex]Option B is correct
Option C is wrong
[tex][/tex]write a part to part and a part to whole ratio for each problem situation of the 31 students surveyed 19 prefer white bread and the remaining students prefer wheat bread
Total number of students = 31
19 prefer white bread
31 - 19 prefer wheat bread ==> 31- 19 = 12 prefer wheat bread
Relations:
Part to part:
Relation between the number of students that prefer wheat bread to the number of students that prefer white bread:
Ratio: 12/19
Part to part:
Relation between the number of students that prefer white bread to the number of students that prefer white bread:
Ratio: 19/12
Part to whole:
Relation between the number of students that prefer wheat bread to the total number of students:
Ratio: 12/31
Part to whole:
Relation between the number of students that prefer white bread to the total number of students:
Ratio: 19/31
solve the equation Mentally
Given:-
[tex]\begin{gathered} 8+j=15 \\ \end{gathered}[/tex]To Find:-
The value of j.
To find the value of j, we need to keep j at one side of the equal to sign and take all other number to the other side of the equal to sign.
[tex]\begin{gathered} 8+j=15 \\ j=15-8 \\ j=7 \end{gathered}[/tex]So now the value of j has been found. The value of j is 7.
Find the degree of the polynomial f(x) = x6 + x2 + 5x.A.5B.6C.-5D.-6
To find the degree of a polynomial identify the greater exponent, that is the degree of the polynomial.
In the given polynomial the greater exponent is 6, then it is degree 6Answer: 6Charlotte has $6,367 in a savings account. The interest rate is 14%, compounded annually.To the nearest cent, how much will she have in 4 years?
Solution
Given the savings account, and solve for the interest:
Principal = $6,367
Interest rate = 14%
time = 4years
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]First, convert R as a percent to r as a decimal
r = R/100
r = 14/100
r = 0.14 rate per year,
Then solve the equation for A
[tex]A=P(1+\frac{r}{n})^{nt}[/tex][tex]\begin{gathered} A=6367(1+\frac{0.14}{1})^{(1)(4)} \\ A=6367(1+0.14)^4 \\ A=10753.61 \end{gathered}[/tex]A = $10,753.61
Therefore the correct answer is $10,753.61 (nearest cent)
Find the range of the graphed function.A. -9 < y < 5B. y is all real numbers.C. O < y < 10D. y > 0
The range of a function is all the values that the function can take on the y-axis.
So, the y values of this function are between -9 and 5.
It means that the range is:
A. -9 < y < 5
What is the area of this trapezoid? 13 ft Enter your answer in the box. 16 ft ft2 31 ft
The area of a trapezoid is given as
[tex]A=\frac{1}{2}(a+b)h[/tex]From the given trapezoid
[tex]a=13ft,b=31ft,h=16ft[/tex]Substitute the values of a, b, and h into the equation
This gives
[tex]A=\frac{1}{2}(13+31)\times16[/tex]Calculate the value of A
[tex]\begin{gathered} A=\frac{1}{2}(44)\times16 \\ A=44\times8 \\ A=352 \end{gathered}[/tex]Therefore the area of the trapezoid is
[tex]352ft^2[/tex]Answer:
Your answer would be 352ft²
Step-by-step explanation:
I took the test and got 100%
Exhibit 6-4The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000.Refer to Exhibit 6-4. What is the probability that a randomly selected individual with an MBA degree will get a starting salary of at least $30,000?
Given:
Normally distributed = $40,000
a standard deviation= $5,000.
Required:
Find the probability that a randomly selected individual with an MBA degree will get a starting salary of at least $30,000.
Explanation:
The probability formula when the mean and standard deviation is known:
[tex]P(x)=P(\frac{x-mean}{standard\text{ deviation}})[/tex][tex]\begin{gathered} P(x\ge30k)=P(\frac{30k-40k}{5k}) \\ \begin{equation*} P(x\ge30k)= \end{equation*} \end{gathered}[/tex]
What linear equation represents the graph of a horizontal line, parallel to the Z-axis, that travels through the point (0,4)? Use the grid or a piece of paper if needed.
Problem
What linear equation represents the graph of a horizontal line, parallel to the Z-axis, that travels through the point (0,4)? Use the grid or a piece of paper if needed.
Solution
for this case the general equation of a plane is given by:
A(x-xo) + B(y-yo) + C(z-zo)=0
C=0 for this case
A(x-xo) + B(y-yo) =0
And for this case one possible answer would be:
y=4
Which of the following graphs shows a positive linear relationship with acorrelation coefficient, r, close to 1?A.B.D.A. Graph AОСB. Graph BO C. Graph CO D. Graph DPREVIOUSreAOO
Given:
The objective is to choose the correct graph which shows a positive linear relationship with a correlation coefficient, r, close to 1.
The positive linear relationship represents the increasing values of plots from origin to positive x and positive y axis.
By observing graph A, the plots are scattered all over the quadrant. Hence, it is a weak association.
By observing graph B, the plots are plotted as decreasing in y axis and increasing in x axis. Hence, it is a strong negative association.
By observing graph C, the plots are plotted as increasing in both x axis and y axis. Hence, it is a strong positive association.
Hence, the graph which shows a positive linear relationship with a correlation coefficient, r, close to 1 is graph C.
For which of the following displays of data is it not possible to find the mean?histogramfrequency tablestem-and-leaf plotdot plot
Simplify: which of the following displays of data is it not possible to find the mean?
(a) histogram
(b) frequency table
(c) stem-and-leaf plot
(d) dot plot
Explanation: (a) histogram is correct answer because by using histogram it is not possible to find exact mean and median value.
Final answer: (a) histogram data is it not possible to find the mean.
I just really need help I don’t know that much about math I was in special Ed math and got kicked out I just need help and need to be shown what I’m doing
Given:
15 pounds of barrel
10 gallons of water; 98.4 pounds
20 gallons of water; 181.8 pounds
In order to find the equation and graph that matches this, we need to find the following:
y - intercept
slope of the line
In the problem, it was given that the barrel weighs 15 pounds. Meaning, even in an empty barrel, we already have a total weight of 15 pounds.
We let:
x = gallons of water
y = total weight
This means, at x = 0, y = 15.
y - i
consider a parabola that intersects the x axis at points (-1,0) and (3,0)
Given that we only have two points known in the parabola, the best way to determine the equation (having the options already) is to substitute the points on each equation to see which one is true for both points:
[tex]\begin{gathered} y=x^2+3x+2 \\ \text{for (-1,0)}\colon \\ 0=(-1)^2+3(-1)+2 \\ \Rightarrow0=1-3+2=3-3=0 \\ \text{for (3,0)}\colon \\ \Rightarrow0=(3)^2+3(3)+2=9+9+2=20 \end{gathered}[/tex]As we can see on the previous example, when we substitute the point (3,0), we get a contradiction, since 0=20 can never happen. Working this way we find that the equation y=x^2-2x-3 yields the desired results:
[tex]\begin{gathered} y=x^2-2x-3 \\ on\text{ (-1,0):} \\ 0=(-1)^2-2(-1)+3=1+2-3=0 \\ on\text{ (3,0):} \\ 0=(3)^2-2(3)-3=9-6-3=9-9=0 \end{gathered}[/tex]Therefore, the equation of the parabola is y=x^2-2x-3