# How do you write the quadratic equation given Vertex: (1/2, 1/2) Passing though: (3/4, 1/4)?

Sep 4, 2017

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

#### Explanation:

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

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

$\text{here } \left(h , k\right) = \left(\frac{1}{2} , \frac{1}{2}\right)$

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

$\text{to find a substitute "(3/4,1/4)" into the equation}$

$\frac{1}{4} = \frac{1}{16} a + \frac{1}{2} \Rightarrow a = - 4$

$\Rightarrow y = - 4 {\left(x - \frac{1}{2}\right)}^{2} + \frac{1}{2} \leftarrow \textcolor{red}{\text{ in vertex form}}$

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