# How do you write a quadratic equation with vertex; ( 0,1 ); point: ( 1,3 )?

May 18, 2017

$y = 2 {x}^{2} + 1$

#### Explanation:

$\text{the equation of a quadratic function in "color(blue)"vertex form}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = a {\left(x - h\right)}^{2} + k} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where ( h , k ) are the coordinates of the vertex and a is a constant.

$\text{here } \left(h , k\right) = \left(0 , 1\right)$

$\Rightarrow y = a {\left(x - 0\right)}^{2} + 1$

$\Rightarrow y = a {x}^{2} + 1$

$\text{to find a, substitute " (1,3)" into the equation}$

$\Rightarrow 3 = a + 1 \Rightarrow a = 2$

$\Rightarrow y = 2 {x}^{2} + 1 \leftarrow \textcolor{red}{\text{ in vertex form}}$
graph{2x^2+1 [-10, 10, -5, 5]}