What is the axis of symmetry and vertex for the graph #y=x^2+5x-7#?

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Answer 1 · 2017-03-17T04:41:30

Vertex #rArr (-5/2,-53/4)#

Axis of Symmetry# rArr x =-5/2 #

Method 1-
The graph of # y=x^2+5x-7# is -
graph{x^2+5x-7 [-26.02, 25.3, -14.33, 11.34]}
According to the above graph, We can find the vertex and axis of symmetry of the above graph.
Vertex #rArr (-5/2,-53/4)#
Axis of Symmetry# rArr x =-5/2 #
Method 2-

Check the derivative of the function.

# y=x^2+5x-7#

#y' = dy/dx = 2x+5#

The derivative of the function is zero at its vertex .

#y' = 2x+5 = 0#

#x=-5/2#

Put the #x=-5/2# in the function to get the value of the function at #x=-5/2#.

# y=25/4-25/2-7#

# y=(25-50-28)/4#

#y = -53/4#

Vertex #rArr (-5/2,-53/4)#

Axis of Symmetry# rArr x =-5/2 #

The given function is a quadratic function.

# y=x^2+5x-7#

The vertex of the parabola of the quadratic function #= (-b/(2a), -D/(4a))#

#= (-5/(2), -53/(4))#

Axis of Symmetry# rArr x =-5/2 #