# How do you write a quadratic function in vertex form whose graph has the vertex (1, 8) and passes through the point (3, 12)?

Jun 14, 2018

$y = {\left(x - 1\right)}^{2} + 8$

#### Explanation:

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

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = a {\left(x - h\right)}^{2} + k} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{where "(h,k)" are the coordinates of the vertex and a}$
$\text{is a multiplier}$

$\text{here } \left(h , k\right) = \left(1 , 8\right)$

$y = a {\left(x - 1\right)}^{2} + 8$

$\text{to find a substitute "(3,12)" into the equation}$

$12 = 4 a + 8$

$12 - 8 = 4 a \Rightarrow 4 a = 4 \Rightarrow a = 1$

$y = {\left(x - 1\right)}^{2} + 8 \leftarrow \textcolor{red}{\text{in vertex form}}$
graph{(x-1)^2+8 [-28.87, 28.86, -14.43, 14.44]}