# How do you find the standard equation given vertex at (0,-1) and passes through the point (2,2)?

##### 1 Answer
Aug 10, 2017

$y = \frac{3}{4} {x}^{2} - 1$

#### Explanation:

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

$\text{here "h=0" and } k = - 1$

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

$\text{to find a use the point "(2,2)" in the equation}$

$2 = 4 a - 1 \Rightarrow a = \frac{3}{4}$

$\Rightarrow y = \frac{3}{4} {x}^{2} - 1 \leftarrow \textcolor{red}{\text{ in standard form}}$