Question

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

Answer 1

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

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

Explanation:

• 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`

• 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`