Question

Question 7b: Let g(x) be a polynomial function. Name all horizontal andvertical intercepts of the graphsg(x) = (x - 1)2 (x + 2)Horizontal intercepts: 1, -2; vertical intercepts: 2Horizontal intercepts: 2, vertical intercepts: 1,-2Horizontal intercepts: -1, 2, vertical intercepts: 4Horizontal intercepts: 4, vertical intercepts: -1,2

Answer 1

The given function is expressed as

g(x) = (x - 1)^2(x + 1)

It can be written as

y = (x - 1)^2(x + 1)

The horizontal intercept is also known as the x intercept. The x intercept is the value of x when y = 0

If we substitute y = 0 into the function, it becomes

0 = (x - 1)^2(x + 2)

This means that

(x - 1)^2 = 0 and x + 2 = 0

For (x - 1)^2 = 0, if we take the square root of both sides, it becomes

x - 1 = 0

x = 1

For x + 2 = 0,

x = - 2

Thus, the horizontal intercepts are 1 and - 2

The vertical intercept is also known as the y intercept. The y intercept is the value of y when x = 0

If we substitute x = 0 into the function, it becomes

y = (0 - 1)^2(0 + 2)

y = (- 1)^2(2)

y = 1 * 2 = 2

Thus, the vertical intercept is 2

Thus, the correct option is

Horizontal intercepts: 1, -2; vertical intercepts: 2