What is the axis of symmetry and vertex for the graph y=x^2+5x-7y=x2+5x7?

1 Answer
Mar 17, 2017

Vertex rArr (-5/2,-53/4)(52,534)

Axis of Symmetry rArr x =-5/2 x=52

Explanation:

  • Method 1-
    The graph of y=x^2+5x-7y=x2+5x7 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)(52,534)
    Axis of Symmetry rArr x =-5/2 x=52

  • Method 2-

Check the derivative of the function.

y=x^2+5x-7y=x2+5x7

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

  • Method 3-

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