Final answer:
The y-intercept of the function y = x² - 9 is (0, -9), and the x-intercepts are (-3, 0) and (3, 0) after setting y to 0 and solving for x.
Step-by-step explanation:
The student is asking about the x and y intercepts of the quadratic function y = x² - 9. To find the y-intercept, we set x to zero and solve for y. This yields:
y = (0)² - 9 = -9
So, the y-intercept is (0, -9). To find the x-intercepts, we set y to zero and solve for x:
0 = x² - 9
x² = 9
x = ±√9
x = ±3
Hence, the x-intercepts are (-3, 0) and (3, 0).