Question

1. A quadratic function fis defined by f(x) = (x - 7)(x + 3).

a. Without graphing, identify the x-intercepts of the graph of f. ( , ) and ( , )

b. If x=___, then (____- 7) = 0. If x = ____, then (____+ 3) = 0

c. Expand (x - 7)(x + 3) and use the expanded form to identify the y-intercept of the graph of f. Show work
Expanded form f (x) =_______
y-intercept ( , )

Answer 1

a) (-3, 0) and (7, 0)

b) If x = 7 then (7 - 7) = 0

If x = -3 then (-3 + 3) = 0

c) f(x) = x² - 4x - 21

y-intercept (0, -21)

Explanation:

a)

x-intercepts are when f(x) = 0

Therefore, if f(x) = (x - 7)(x + 3) then (x - 7)(x + 3) = 0

⇒ x - 7 = 0

⇒ x = 7

and

⇒ x + 3 = 0

⇒ x = -3

So x-intercepts are (-3, 0) and (7, 0)

b) If x = 7 then (7 - 7) = 0

If x = -3 then (-3 + 3) = 0

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

⇒ f(x) = x² + 3x - 7x - 21

⇒ f(x) = x² - 4x - 21

The y-intercept is when x = 0 ⇒ (0, -21)