# How do you find the axis of symmetry, and the maximum or minimum value of the function #y=x^2+5x-7#?

##### 1 Answer

Mar 14, 2017

#### Explanation:

For the standard equation of a parabola.

#• y=ax^2+bx+c#

#• " has a minimum if "a>0" that is " uuu#

#• "has a maximum if "a<0" that is "nnn#

#"for "y=x^2+5x-7,a=1,b=5,c=-7#

#"Since "a>0" then parabola has a minimum"#

#x_(color(red)"vertex")=-b/(2a)=-5/2# Substitute this value into the function for

#y_("vertex")#

#rArry_(color(red)"vertex")=(-5/2)^2+(5xx-5/2)-7#

#color(white)("rArry_("ve)=25/4-50/4-28/4#

#color(white)(xxxxxx)=-53/4# The vertex has coordinates

#(-5/2,-53/4)# The axis of symmetry passes through the vertex and is vertical.

#rArr"axis of symmetry is "x=-5/2#

#"and minimum value "=-53/4#

graph{(y-x^2-5x+7)(y-1000x-2500)=0 [-28.85, 28.89, -14.42, 14.44]}