Answer:
The y-intercept is the point (0, 128).
The x-intercepts are the points (-4, 0) and (-8, 0).
As x → ∞, y → ∞.
As x → -∞, y → -∞.
Explanation:
To find the y-intercept, substitute 0 for x and solve for y.
- P(x) = (x + 4)²(x + 8)
- P(0) = (0 + 4)²(0 + 8)
- P(0) = (4)²(8)
- P(0) = 16 * 8
- P(0) = 128
The y-intercept is (0, 128).
To find the x-intercept, substitute 0 for y and solve for x.
Set the first term, (x + 4)², equal to 0.
- 0 = (x + 4)²
- 0 = x + 4
- -4 = x
- x = -4
Set the second term, (x + 8), equal to 0.
The x-intercepts are the point (-4, 0) and (-8, 0).
Look at the degree and leading coefficient of the polynomial to determine the end behavior, and therefore you can determine how y behaves as x gets closer to infinity.
Since the degree of the polynomial is odd (3) and the leading coefficient is positive, the graph falls to the left and rises to the right.
So, as x → ∞, y → ∞ and as x → -∞, y → -∞.
If you want to verify this, plug the equation into your calculator and look at the graph. How does it behave as you look at negative x-values? How about for positive x-values?