Question

.Find the vertex, zero(s), and y-intercept of the graph of y = x2 + 4x – 5.

Answer 1

The vertex is;

(-2,-9)

The zeroes are;

x=-5,x=1

Y-intercept: (0,-5)

EXPLANATION

Given:

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

Complete the square to obtain,

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

`y =( {x + 2) }^(2) - 9`

The vertex of this function is ;

(-2,-9)

To find the zeroes, we equate y to zero.

`( {x + 2) }^(2) - 9 = 0`

`( {x + 2) }^(2) = 9`

`x + 2 = \pm √(9)`

`x = - 2 \pm 3`

`x = - 5\: or \: x = 1`

The y-intercept is

`y = {0}^(2) + 4(0)- 5 = - 5`

The y-intercept has coordinate

(0,-5)

Answer 2

Vertex (-2,-9)

zeros: x=1, x=-5

y-intercept: -5

Explanation:

When you graph the quadratic equation you obtain the parabola shown in the figure attached.

Find the vertex of the parabola observing the graph, you can that the minimum point of the parabola is at (-2,-9) this is the vertex.

The zeros are the x-intercepts:

x=1; x=-5

And the y-intecept is when x=0 and the parabola cut the y-axis. This is: -5.