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

Question

a) Write the equation in factored form

Answer 1

To write the equation in factored form, we need to first factor out the coefficient of the squared term, which is 1:

y = x^2 - 10x + 16

Next, we need to find two numbers that multiply to 16 and add up to -10 (the coefficient of the x term). These numbers are -2 and -8:

y = (x - 2)(x - 8)

Therefore, the equation in factored form is y = (x - 2)(x - 8).