Question

What is the vertex form of the quadratic function that has a vertex at (2,1)and goes through the point (3,-2)?

Answer 1

Concept

Apply the equation of the vertex form below to write the quadratic function.

`y=a(x-h)^2\text{ + k}`

Next,

where

(x,y) is any point on the described parabola, (h,k) is the vertex of the parabola, and a is an unknown value that is found using the given point that is not the vertex.

The vertex is ( h, k ) = ( 2, 1 )

( x, y ) = ( 3 , -2 )

Next, substitute h, k , x and y in the equation to find the value of a.

`\begin{gathered} y\text{ = a(x - }h)^2\text{ + }k \\ -2=a(3-2)^2\text{ + 1} \\ \text{collect like terms} \\ -\text{ 2 - 1 = a }*1^2 \\ -\text{ 3 = a} \end{gathered}`

Final answer

Substitute the values of h, k and a in the original equation.

`y=-3(x-2)^2\text{ + 1}`