188k views
3 votes
What is the vertex form equation of a parabola with vertex (2, -5) that goes through point (-2, 7)

2 Answers

3 votes

Answer:


y=(3)/(4)(x-2)^2-5

Explanation:


\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}

Given:

  • Vertex = (2, -5)
  • Point = (-2, 7)

Substitute the given vertex and point into the formula and solve for a:


\implies 7=a(-2-2)^2+(-5)


\implies 7=a(-4)^2-5


\implies 7=16a-5


\implies 12=16a


\implies a=(12)/(16)


\implies a=(3)/(4)

Substitute the vertex and the found value of a into the formula to create an equation in vertex form for the given parameters:


y=(3)/(4)(x-2)^2-5

User Yaakov Belch
by
8.7k points
3 votes

Answer:

y =
(3)/(4) (x - 2)² - 5

Explanation:

the equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

here (h, k ) = (2, - 5 ) , then

y = a(x - 2)² - 5

to find a substitute (- 2, 7 ) into the equation

7 = a(- 2 - 2)² - 5 ( add 5 to both sides )

12 = a(- 4)² = 16a ( divide both sides by 16 )


(12)/(16) = a , that is a =
(3)/(4)

y =
(3)/(4) (x - 2)² - 5 ← equation in vertex form

User Bcause
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories