# How do you find the axis of symmetry, and the maximum or minimum value of the function  y=-x^2-3x+2?

Sep 3, 2017

$x = - \frac{3}{2} , \text{max. value } = \frac{17}{4}$

#### Explanation:

$\text{the axis of symmetry passes through the vertex}$

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

$\text{to express the parabola in this form "color(blue)"complete the square}$

$y = - \left({x}^{2} + 3 x - 2\right) \leftarrow \text{ coefficient of } {x}^{2} = 1$

$\Rightarrow y = - \left({x}^{2} + 2 \left(\frac{3}{2}\right) x + \frac{9}{4} - \frac{9}{4} - 2\right)$

$\textcolor{w h i t e}{\Rightarrow y} = - {\left(x + \frac{3}{2}\right)}^{2} + \frac{17}{4}$

$\text{axis of symmetry is } x = h \Rightarrow x = - \frac{3}{2}$

$\text{since "a<0" then graph is a maximum } \bigcap$

$\text{since } {\left(x + \frac{3}{2}\right)}^{2} \ge 0$

$\Rightarrow \text{maximum value } = \frac{17}{4}$