CPM Homework Help : A2C Problem 10-148

Given the function h(x) = 2(x + 3)² + 2: Homework Help ✎
1. What are the intercepts?
2. What are the domain and range?

Step 1(a):

To find the y-intercept, substitute 0 for x.

h(0) = −2(9) + 2

Step 2(a):

To find the x-intercept substitute 0 for h(x).

0 = −2(x + 3)² + 2

Step 3(a):

−2(x + 3)² = −2

Step 4(a):

(x + 3)² = 1

Step 5(a):

x + 3 = ± 1

Answer 1 (a):

y-intercept (0, −16)

Answer 2(a):

x-intercept (−4, 0), (−2, 0)

Hint (b):

Which variable is being squared?

Answer (b):

Domain: all real numbers
Range: y ≤ 2