Question

Find the x intercept (s) and the coordinates of the vertex for the parabola y= x^2 -4x -5. If there is more than one X intercept, separate them with commas

Answer 1

• x-intercepts: -1, 5
• vertex: (2, -9)

Explanation:

The factors of -5 that add to give -4 are -5 and +1. So, the equation can be factored as ...

y = (x -5)(x +1)

The x-intercepts are the values of x that make these factors be zero.

x = 5 makes the first factor 0

x = -1 makes the second factor 0

The x-intercepts are x = -1, 5.

__

The x-coordinate of the vertex is halfway between the x-intercepts, so can be found by averaging their values.

vertex x-coordinate = (-1 +5)/2 = 2

The y-coordinate of the vertex is the value of y for that value of x:

y = (2 -5)(2 +1) = (-3)(3) = -9 . . . . . filling x=2 into the factored equation

The vertex is (x, y) = (2, -9).

_____

A graphing calculator can confirm these values for you.