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

##### 1 Answer

Sep 3, 2017

#### Explanation:

#"the axis of symmetry passes through the vertex"#

#"the equation of a parabola in "color(blue)"vertex form"# is.

#color(red)(bar(ul(|color(white)(2/2)color(black)(y=a(x-h)^2+k)color(white)(2/2)|)))#

where (h , k ) are the coordinates of the vertex and a is a constant.

#y=-(x^2+3x-2)larr" coefficient of "x^2=1#

#rArry=-(x^2+2(3/2)x+9/4-9/4-2)#

#color(white)(rArry)=-(x+3/2)^2+17/4#

#"axis of symmetry is "x=hrArrx=-3/2#

#"since "a<0" then graph is a maximum "nnn#

#"since "(x+3/2)^2>=0#

#rArr"maximum value "=17/4#