Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

IXI.com Play Gimkit! - Ent... adjunct - Google... root word bi mea.. Audio Converter: IXL -W My IXL Learning Assessment Analytics Algebra 1 > *** Y. Write a quadratic function from its x-intercepts and another point UDD You have Write the equation of the parabola that passes through the points shown in the table. x y -2 0 6 0 7 27 Write your answer in the form y=a(x-p)(x-q), where a,p, and q are integers, decimals, or simplified fractions. Submit Work it out Not feeling ready yet? These can help: Solve one-step linear equations Lesson: Quadratic equations Practice in the app

IXI.com\newlinePlay Gimkit! - Ent...\newlineadjunct - Google...\newlineroot word bi mea..\newlineAudio Converter:\newlineIXL \mathrm{IXL} \newline−W -\mathrm{W} \newlineMy IXL\newlineLearning\newlineAssessment\newlineAnalytics\newlineAlgebra 1>\star Y. Write a quadratic function from its x x -intercepts and another point UDD\newlineYou have\newlineWrite the equation of the parabola that passes through the points shown in the table.\newline\begin{tabular}{|c|c|}\newline\hlinex x & y y \\\newline\hline−2-2 & 00 \\\newline\hline 66 & 00 \\\newline\hline 77 & 2727 \\\newline\hline\newline\end{tabular}\newlineWrite your answer in the form y=a(x−p)(x−q) \mathrm{y}=\mathrm{a}(\mathrm{x}-\mathrm{p})(\mathrm{x}-\mathrm{q}) , where a,p \mathrm{a}, \mathrm{p} , and q \mathrm{q} are integers, decimals, or simplified fractions.\newlineSubmit\newlineWork it out\newlineNot feeling ready yet? These can help:\newlineSolve one-step linear equations\newlineLesson: Quadratic equations\newlinePractice in the app

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Compare linear and exponential growthright chevron icon

Full solution

Q. IXI.com\newlinePlay Gimkit! - Ent...\newlineadjunct - Google...\newlineroot word bi mea..\newlineAudio Converter:\newlineIXL \mathrm{IXL} \newline−W -\mathrm{W} \newlineMy IXL\newlineLearning\newlineAssessment\newlineAnalytics\newlineAlgebra 1>⋆ 1>\star Y. Write a quadratic function from its x x -intercepts and another point UDD\newlineYou have\newlineWrite the equation of the parabola that passes through the points shown in the table.\newline\begin{tabular}{|c|c|}\newline\hlinex x & y y \\\newline\hline−2-2 & 00 \\\newline\hline 66 & 00 \\\newline\hline 77 & 2727 \\\newline\hline\newline\end{tabular}\newlineWrite your answer in the form y=a(x−p)(x−q) \mathrm{y}=\mathrm{a}(\mathrm{x}-\mathrm{p})(\mathrm{x}-\mathrm{q}) , where a,p \mathrm{a}, \mathrm{p} , and q \mathrm{q} are integers, decimals, or simplified fractions.\newlineSubmit\newlineWork it out\newlineNot feeling ready yet? These can help:\newlineSolve one-step linear equations\newlineLesson: Quadratic equations\newlinePractice in the app
  1. Identify Points: Identify the xx-intercepts and another point given.\newlineThe xx-intercepts are the points where the parabola crosses the xx-axis, which means y=0y=0. From the table, we can see that the xx-intercepts are x=−2x=-2 and x=6x=6. The other point given is (7,27)(7, 27).
  2. Write Factored Form: Use the x-intercepts to write the factored form of the quadratic function.\newlineThe factored form of a quadratic function with x-intercepts pp and qq is y=a(x−p)(x−q)y=a(x-p)(x-q). In this case, p=−2p=-2 and q=6q=6, so the equation becomes y=a(x+2)(x−6)y=a(x+2)(x-6).
  3. Solve for Coefficient: Use the third point to solve for the coefficient aa. We have the point (7,27)(7, 27), which means when x=7x=7, y=27y=27. We can substitute these values into the equation y=a(x+2)(x−6)y=a(x+2)(x-6) to find aa. 27=a(7+2)(7−6)27 = a(7+2)(7-6) 27=a(9)(1)27 = a(9)(1) 27=9a27 = 9a a=279a = \frac{27}{9} (7,27)(7, 27)00
  4. Final Equation: Write the final equation of the parabola.\newlineNow that we have found a=3a=3, we can write the final equation of the parabola:\newliney=3(x+2)(x−6)y = 3(x+2)(x-6)

More problems from Compare linear and exponential growth

Question
Jill bought a used motorcycle from a seller online for $1,200. The seller will charge her $5 a day to store the motorcycle at his house until she is able to pick it up. You can use a function to describe the total amount of money Jill will owe the seller if she waits xx days to pick up the motorcycle.\newlineWrite an equation for the function. If it is linear, write it in the form g(x)=mx+bg(x) = mx + b. If it is exponential, write it in the form g(x)=a(b)xg(x) = a(b)^x.\newlineg(x)=‾g(x) = \underline{\hspace{3em}}
Get tutor helpright-arrow

Posted 5 months ago

Question
How does f(t)=−2t−7f(t)=-2t-7 change over the interval from t=−7t=-7 to t=−6t=-6?\newlineChoices:\newline[f(t) decreases by 2]\left[\text{f(t) decreases by } 2\right]\newline[f(t) increases by 2]\left[\text{f(t) increases by } 2\right]\newline[f(t) increases by 200%]\left[\text{f(t) increases by } 200\%\right]\newline[f(t) decreases by a factor of 2]\left[\text{f(t) decreases by a factor of } 2\right]
Get tutor helpright-arrow

Posted 5 months ago

Question
How does g(t)=9tg(t)=9^t change over the interval from t=1t=1 to t=3t=3?\newlineChoices: \newline[g(t) decreases by a factor of 81]\left[\text{g(t) decreases by a factor of } 81\right]\newline[g(t) increases by a factor of 81]\left[\text{g(t) increases by a factor of } 81\right]\newline[g(t) increases by 18%]\left[\text{g(t) increases by } 18\%\right]\newline[g(t) decreases by 9%]\left[\text{g(t) decreases by } 9\%\right]
Get tutor helpright-arrow

Posted 5 months ago

Question
Both of these functions grow as xx gets larger and larger. Which function eventually exceeds the other?\newline Choices:\newline(A)f(x)=8x+3.3(A)f(x) = 8x + 3.3\newline(B)g(x)=3.3x−5(B)g(x) = 3.3^x - 5
Get tutor helpright-arrow

Posted 6 months ago

Question
Both of these functions grow as x x gets larger and larger. Which function eventually exceeds the other?\newlineChoices:\newline(A) f(x)=2x+9(A) \ f(x) = 2x + 9 \newline(B) g(x)=2x(B)\ g(x) = 2^x
Get tutor helpright-arrow

Posted 6 months ago

Question
The functions f(x) f(x) and g(x) g(x) are differentiable. \newlineThe function h(x) h(x) is defined as: h(x)=g(x)f(x) h(x)=\frac{g(x)}{f(x)} \newlineIf f(8)=1 f(8)=1 , f′(8)=−6 f'(8)=-6 , g(8)=8 g(8)=8 , and g′(8)=−10 g'(8)=-10 , what is h′(8) h'(8) ? \newlineSimplify any fractions. \newlineh′(8)= h'(8)= ______
Get tutor helpright-arrow

Posted 6 months ago

Question
The functions p(x) p(x) and q(x) q(x) are differentiable. \newlineThe function r(x) r(x) is defined as: r(x)=p(x)q(x) r(x)= \frac{p(x)}{q(x)} \newlineIf p(3)=2 p(3)= 2 , p′(3)=4 p'(3)= 4 , q(3)=6 q(3)= 6 , and q′(3)=9 q'(3)= 9 , what is r′(3) r'(3) ? \newlineSimplify any fractions. \newliner′(3)= r'(3)= _____
Get tutor helpright-arrow

Posted 7 months ago

Question
The functions u(x) u(x) and v(x) v(x) are differentiable. \newlineThe function w(x) w(x) is defined as: w(x)=u(x)v(x) w(x)= \frac{u(x)}{v(x)} \newlineIf u(5)=3 u(5)= 3 , u′(5)=−2 u'(5)= -2 , v(5)=7 v(5)= 7 , and v′(5)=1 v'(5)= 1 , what is w′(5) w'(5) ? \newlineSimplify any fractions. \newlinew′(5)= w'(5)= _____
Get tutor helpright-arrow

Posted 7 months ago

Question
The functions a(x) a(x) and b(x) b(x) are differentiable. \newlineThe function c(x) c(x) is defined as: c(x)=a(x)b(x) c(x)= \frac{a(x)}{b(x)} \newlineIf a(2)=4 a(2)= 4 , a′(2)=5 a'(2)= 5 , b(2)=1 b(2)= 1 , and b′(2)=−3 b'(2)= -3 , what is c′(2) c'(2) ? \newlineSimplify any fractions. \newlinec′(2)= c'(2)= _____
Get tutor helpright-arrow

Posted 7 months ago

Question
The functions m(x) m(x) and n(x) n(x) are differentiable. \newlineThe function o(x) o(x) is defined as: o(x)=m(x)n(x) o(x)= \frac{m(x)}{n(x)} \newlineIf m(7)=2 m(7)= 2 , m′(7)=−1 m'(7)= -1 , n(7)=4 n(7)= 4 , and n′(7)=8 n'(7)= 8 , what is o′(7) o'(7) ? \newlineSimplify any fractions. \newlineo′(7)= o'(7)= _____
Get tutor helpright-arrow

Posted 7 months ago

View all (427)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant