Question

The steps in writing f(x) = 18x + 3x2 in vertex form are shown, but a value is missing in the last step. Write the function in standard form. f(x) = 3x2 + 18x Factor a out of the first two terms. f(x) = 3(x2 + 6x) Form a perfect square trinomial. f(x) = 3(x2 + 6x + 9) – 3(9) Write the trinomial as a binomial squared. f(x) = 3(x + ______)2 – 27 What is the missing value in the last step?

Answer 1

y = 3x² + 18x

factor out the leading coefficient
y = 3(x²+6x)

Complete the square
 coefficient of the x term: 6
 divide it in half: 3
 square it: 3²
 use 3² to complete the square:
y = 3(x²+6x + 3²) - 3·3²
 = 3(x+3)² - 3·3²
 = 3(x+3)² - 27
vertex (-3, -27)

Answer 2

the answer would be 3