Question

How do you write a quadratic equation with vertex; ( 0,-3 ); point: ( 2,5 ) ?

Answer 1

`y = 2x^2 - 3`

Explanation:

The quadratic function in vertex form is

`y = a(x - h)^2 + k`

where (h , k) are the coords of the vertex and a is a constant.

here the vertex is (0 , -3) and substituting these values into the function gives.

`y =a (x - 0)^2 - 3 → y = ax^2 - 3`

To find the value of a , we use the point (2 , 5) and substitute into the function.

x = 2 , y = 5 : `a(2)^2 - 3 = 5 → 4a = 8 → a = 2`

`rArr color(red)(|bar(ul(color(white)(a/a)color(black)(y = 2x^2 - 3)color(white)(a/a)|)))`

This is the graph of `y = 2x^2 - 3`
graph{2x^2-3 [-10, 10, -5, 5]}