How do you find the axis of symmetry, and the maximum or minimum value of the function #y=x^2+3x-5#?

1 Answer
Apr 23, 2018

The axis of symmetry is #x=-3/2# or #-1.5#.

The vertex is #(-3/2,-29/4)# or #(-1.5,-7.25)#.

Explanation:

Given:

#y=x^2+3x-5# is a quadratic equation in standard form:

#y=ax^2+bx+c#,

where:

#a=1#, #b=3#, #c=-5#

Axis of symmetry: vertical line that divides the parabola into two equal halves. It is also the #x#-coordinate of the vertex.

The formula to find the axis of symmetry:

#x=(-b)/(2a)#

Plug in the known values.

#x=(-3)/(2*1)#

#x=-3/2# or #-1.5#

The axis of symmetry is #x=-3/2# or #-1.5#.

Vertex: the minimum or maximum point on the parabola. The axis of symmetry is the #x#-coordinate. To find the #y#-coordinate, substitute #-3/2# into the equation and solve for #y#.

#y=(-3/2)^2+3(-3/2)-5#

#y=9/4-9/2-5#

Multiply #9/2# by #2/2#, and #5# by #4/4# so each term has #4# as its denominator.

#y=9/4-9/2xxcolor(red)2/color(red)2-5xxcolor(green)4/color(green)4#

#y=9/4-18/4-20/4#

Simplify.

#y=((9-18-20))/4#

#y=-29/4#

The vertex is #(-3/2,-29/4)# or #(-1.5,-7.25)#.

graph{y=x^2+3x-5 [-16.02, 16.01, -8.01, 8.01]}