Question

The first three steps in writing f(x) = 40x + 5x2 in vertex form are shown. Write the function in standard form. f(x) = 5x2 + 40x Factor a out of the first two terms. f(x) = 5(x2 + 8x) Form a perfect square trinomial. = 16 f(x) = 5(x2 + 8x + 16) – 5(16) What is the function written in vertex form? f(x) = 5(x + 4) – 80 f(x) = 5(x + 8) – 80 f(x) = 5(x + 4)2 – 80 f(x) = 5(x + 8)2 – 80

Answer 1

The correct vertex form of the function f(x) = 40x + 5x2 is f(x) = 5(x + 4)^2 - 80, after completing the square process.

Step-by-step explanation:

The student is asking how to write the quadratic function f(x) = 40x + 5x2 in vertex form. The steps provided by the student show the process of completing the square, which is a method used to convert a quadratic equation from standard form to vertex form. The steps include factoring out the coefficient of the x2 term, forming a perfect square trinomial, and then writing the equation in vertex form. Following these steps, the correct vertex form of the function is f(x) = 5(x + 4)2 - 80.

Answer 2

Rewrite f(x) = 40x + 5x2 as f(x) = 5x^2 + 40x

Factor out the 5: f(x) = 5(x^2 + 8x)

Complete the square: f(x) = 5(x^2 + 8x + 16 - 16) = 5(x+4)^2 - 80 (answer)

Step-by-step explanation: