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:

Write the equation of the parabola that passes through the points (−5,−36)(-5,-36), (−3,0)(-3,0), (−2,0)(-2,0). Write your answer in the form y=a(x–p)(x–q)y=a(x–p)(x–q), where aa, pp, and qq are integers, decimals, or simplified fractions.

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Write a quadratic function from its x-intercepts and another pointright chevron icon

Full solution

Q. Write the equation of the parabola that passes through the points (−5,−36)(-5,-36), (−3,0)(-3,0), (−2,0)(-2,0). Write your answer in the form y=a(x–p)(x–q)y=a(x–p)(x–q), where aa, pp, and qq are integers, decimals, or simplified fractions.
  1. Identify x-intercepts: Identify the x-intercepts from the given points. The x-intercepts are where y=0y=0. Points: (−3,0)(-3,0) and (−2,0)(-2,0) are x-intercepts.
  2. Set pp and qq: Set pp and qq as the xx-intercepts. p=−3p = -3, q=−2q = -2. Write the equation in the form y=a(x−p)(x−q)y = a(x - p)(x - q). y=a(x+3)(x+2)y = a(x + 3)(x + 2).
  3. Use point to find 'a': Use the point (−5,−36)(-5,-36) to find the value of 'a'. Substitute x=−5x = -5 and y=−36y = -36 into the equation. −36=a(−5+3)(−5+2)-36 = a(-5 + 3)(-5 + 2). −36=a(−2)(−3)-36 = a(-2)(-3). −36=6a-36 = 6a.
  4. Solve for 'a': Solve for 'a'. −36=6a-36 = 6a. Divide both sides by 66. a=−6a = -6.
  5. Write final equation: Write the final equation using the values of aa, pp, and qq. y=−6(x+3)(x+2)y = -6(x + 3)(x + 2).

More problems from Write a quadratic function from its x-intercepts and another point

Question
The function h h is defined over the real numbers. This table gives a few values of h h .\newline\begin{tabular}{lllll}\newlinex x & −6-6.11 & −6-6.0101 & −6-6.001001 & −5-5.99 \\\newline\hlineh(x) h(x) & −0-0.2525 & −0-0.7474 & −0-0.9898 & −1-1.00\newline\end{tabular}\newlineWhat is a reasonable estimate for lim⁡x→−6h(x) \lim _{x \rightarrow-6} h(x) ?\newlineChoose 11 answer:\newline(A) −6-6\newline(B) −2-2\newline(C) −1-1\newline(D) The limit doesn't exist
Get tutor helpright-arrow

Posted 4 months ago

Question
What is the amplitude of\newlineg(x)=−2sin⁡(π2x−3)+5? g(x)=-2 \sin \left(\frac{\pi}{2} x-3\right)+5 ? \newlineunits
Get tutor helpright-arrow

Posted 3 months ago

Question
What is the amplitude of y=5sin⁡(4x−2)−3 y=5 \sin (4 x-2)-3 ?\newlineunits
Get tutor helpright-arrow

Posted 3 months ago

Question
What is the amplitude of y=−3cos⁡(πx+2)−6? y=-3 \cos (\pi x+2)-6 ? \newlineunits
Get tutor helpright-arrow

Posted 3 months ago

Question
What is the amplitude of y=3sin⁡(2x−1)+4 y=3 \sin (2 x-1)+4 ?\newlineunits
Get tutor helpright-arrow

Posted 3 months ago

Question
What is the period of the function h(x)=−3cos⁡(πx+2)−6? h(x)=-3 \cos (\pi x+2)-6 ? \newlineGive an exact value.\newlineunits
Get tutor helpright-arrow

Posted 3 months ago

Question
What is the period of the function\newlineh(x)=5sin⁡(4x−2)−3 ?  h(x)=5 \sin (4 x-2)-3 \text { ? } \newlineGive an exact value.\newlineunits
Get tutor helpright-arrow

Posted 3 months ago

Question
What is the period of the function g(x)=2cos⁡(7x+5)+1? g(x)=2 \cos (7 x+5)+1 ? \newlineGive an exact value.\newlineunits
Get tutor helpright-arrow

Posted 3 months ago

Question
What is the period of the function f(x)=3sin⁡(2x−1)+4 f(x)=3 \sin (2 x-1)+4 ?\newlineGive an exact value.\newlineunits
Get tutor helpright-arrow

Posted 3 months ago

Question
What is the period of the function f(x)=−4cos⁡(5x−9)−7 f(x)=-4 \cos (5 x-9)-7 ?\newlineGive an exact value.\newlineunits
Get tutor helpright-arrow

Posted 3 months ago

View all (14)