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

Apr 10, 2016

$y = 2 {x}^{2} - 3$

#### Explanation:

The quadratic function in vertex form is

$y = a {\left(x - h\right)}^{2} + k$

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

$\Rightarrow \textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{y = 2 {x}^{2} - 3} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

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