Question

A quadratic function f is defined by /«) = (x - 7)(x + 3).

a. Without graphing, identify the x-intercepts of the graph of f. Explain how you
know.
b. Expand (x - 7)(x + 3) and use the expanded form to identify the y-intercept of
the graph of 1

Answer 1

Explanation:

The two x intercepts are

x - 7 = 0

x = 7

x + 3= 0

x = - 3

The y intercept is just - 7 * 3 = - 21

To prove this more formally

f(x) = (x - 7)(x + 3)

f(x) = x^2 - 7x + 3x - 21

f(x) = x^2 - 4x - 21