Question

100 Points
Name any x-intercepts and y-intercepts in the graph of the function.

Answer 1

The y-intercept is 6

The x-intercepts are -2, -1 and +1

Explanation:

The y-intercept is the value of y when x = 0

y = -3x³ - 6x² + 3x + 6

Sub x = 0,

y = 0 + 0 + 0 + 6

y = 6

The y-intercept is 6

The x-intercept is the value of x when y = 0

y = -3x³ - 6x² + 3x + 6

Sub u = 0,

-3x³ - 6x² + 3x + 6 = 0

⇒ 3x³ + 6x² - 3x - 6 = 0

⇒ x³ + 2x² - x - 2 = 0

⇒ x²(x + 2) -(x + 2) = 0

⇒ (x² -1)(x + 2) = 0

⇒ x² - 1 = 0 or x + 2 = 0

⇒ x² = 1 or x = -2

⇒ x = 1 or

x = -1 or

x = -2

Therefore the x-intercepts are:

x = 1 or

x = -1 or

x = -2