Question

The quadratic equation is

y = x^2 - 4x -5

how do i find the vertex and do the number line ?

Answer 1

(2,-9)

Explanation:

Set the quadratic equal to zero.

`y = {x}^(2) - 4x - 5`

Factor

`(x - 5)(x + 1)`

Set each of these factors to zero

`x - 5 = 0`

and

`x + 1 = 0`

`x = 5`

and

`x = - 1`

Plot the midpoint of the two values.

`( (5 + ( - 1))/(2) ) = 2`

So the middle term is 2 and the other terms are 5 and -1.

Now the vertex is

`2 {}^(2) - 4(2) - 5 = - 9`

So the vertex is

(2,-9)