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

Question

Write the equation in factored form

Answer 1

To write the equation in factored form, we need to factor the quadratic expression 𝑥² − 10𝑥 + 16.

We can do this by finding two numbers that multiply to 16 and add up to -10. These numbers are -2 and -8, since (-2)(-8) = 16 and (-2) + (-8) = -10.

We can then rewrite the quadratic expression as:

𝑥² − 10𝑥 + 16 = (𝑥 − 2)(𝑥 − 8)

Substituting this into the original equation, we get:

𝑦 = (𝑥 − 2)(𝑥 − 8)

So the factored form of the equation is 𝑦 = (𝑥 − 2)(𝑥 − 8).