A parabola is defined by the equation 𝑦 = 𝑥2 − 10𝑥 + 16.
Write the equation in factored form
The first step is to factor out the coefficient of the squared term, which is 1.
𝑦 = 𝑥2 − 10𝑥 + 16
𝑦 = (𝑥 − 8)(𝑥 − 2)
Therefore, the factored form of the equation is:
𝑦 = (𝑥 − 8)(𝑥 − 2)
To write the equation of the parabola in factored form, we need to factorize the quadratic equation 𝑦 = 𝑥^2 - 10𝑥 + 16.
Step 1: Find the two numbers whose product is equal to the constant term (16) and whose sum is equal to the coefficient of the linear term (-10). In this case, the numbers are -2 and -8.
Step 2: Rewrite the equation using the factored form:
𝑦 = (𝑥 - 2)(𝑥 - 8)
Therefore, the equation of the parabola in factored form is 𝑦 = (𝑥 - 2)(𝑥 - 8).