Question

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

Answer 1

`x=-5/2" and minimum value "=-53/4`

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]}