A parabola is defined by the equation 𝑦 = 𝑥2 − 10𝑥 + 16.

Question

Identify the 𝑥-intercepts of the parabola.

Answer 1

To find the x-intercepts, we set y equal to zero:

0 = 𝑥2 − 10𝑥 + 16

We can factor the quadratic equation:

0 = (𝑥 − 2)(𝑥 − 8)

Using the zero product property, we know that either (𝑥 − 2) or (𝑥 − 8) must be equal to zero. So the x-intercepts are:

𝑥 = 2 and 𝑥 = 8.