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

Step-by-step 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.

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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).

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A graphing calculator can confirm these values for you.

2x + 1

Step-by-step explanation:

First subtract 2x2 from 4x2.

4x2 - 2x2 = 2x

Then subtract 1 from 2.

2 - 1 = 1

Now add them together.

2x + 1