Question

Which point is an x-intercept of the quadratic function f(x) = (x + 6)(x – 3)? (0,6) (0,–6) (6,0) (–6,0)

Answer 1

f(x) = (x + 6)(x – 3)

Rewrite as: 

y = (x + 6)(x – 3)

The x-intercept is the point where the curve cuts the x-axis

At the x-intercept, y = 0

0 = (x + 6)(x – 3)

(x + 6)(x – 3) = 0

Either x + 6 = 0  or x - 3 = 0


                x = -6

The x-intercept is  (-6, 0)



Note


 x - 3 = 0

x = 3

The other intercept is (3, 0)

Answer 2

f(x) = (x + 6)(x – 3)

At x-intercept, f(x) = 0

(x + 6)(x – 3) = 0

Apply zero product property:

x + 6 = 0 or x - 3 = 0

x = - 6 or x = 3

Answer: The x-intercepts are (-6, 0) and (3, 0)