Question

What is the y-intercept of the quadratic function f(x) = (x + 3)(x + 6)?

a) (-3,0)
b) (0, -18)
c) (-6,0)
d) (0, 18)

Answer 1

The y-intercept of the quadratic function f(x) = (x + 3)(x + 6) is found by substituting x with 0, which gives us the point (0, 18).

Step-by-step explanation:

To find the y-intercept of the quadratic function f(x) = (x + 3)(x + 6), you need to evaluate the function when x = 0. The y-intercept is the point where the graph of the function intersects the y-axis. At this point, x is always zero. So, we substitute x with 0 in the function:

f(0) = (0 + 3)(0 + 6) = 3 × 6 = 18

Therefore, the y-coordinate of the y-intercept is 18, and since the y-intercept occurs when x = 0, the coordinates of the y-intercept are (0, 18).