Hi please help me with this question please and thank you

Question

List the intercepts of the equation y=x³-8

Answer 1

To find the y-intercept, replace x in the equation with zero.

y = (0)^3 - 8

y = 0 - 8

y = -8

The y-intercept is (0 , -8)

To find the x-intercept(s), replace y in the equation with zero.

0 = x^3 - 8

8 = x^3 Now take the cubed root of both sides of the equation

2 = x

The x-intercept is (2 , 0)

Hope this helps!

Answer 2

To find the y intercept, when x = 0, y is -8, so the y intercept is (0,-8)

To find the x intercepts, when y = 0, you have x^3 - 8 = 0.

That equation is the difference of cubes and can be factored as:

(x - 2)(x^2 + 2x + 4) = 0

one solution would be 2, so the x-intercept is (2,0)

there are no real solutions to x^2 + 2x + 4

Answer 3

Hi Albert B.

y intercept = -8

x intercept = 2

For y = x³ - 8

When x = 0 y = -8

You have the difference of 2 perfect cubes

(x)³ - (2)³

This factors and you can look this up

(x -2)(x² + 2x + 4)

To find the other zeros if any set the factors equal to zero and solve for x can you give that a try just to confirm there are no other real roots?

You can also graph your function at Desmos.com