Question

Write the function in standard form f(x) = -4 (x - 6)^2 + 15

Answer 1

9514 1404 393

Answer:

  f(x) = -4x^2 +48x -129

Step-by-step explanation:

It usually works well to compute the square first. That is, simplify according to the order of operations.

  f(x) = -4(x^2 -12x +36) +15

  f(x) = -4x^2 +48x -144 +15

  f(x) = -4x^2 +48x -129

Answer 2

Answer:

f(x) = -4x² + 48x - 129

Step-by-step explanation:

Given the quadratic function in vertex form, f(x) = -4(x - 6)² + 15:

In order to transform the given function into its standard form, f(x) = ax² + bx + c, expand the squared binomial (without distributing -4 and adding 15).

f(x) = -4(x - 6)² + 15

f(x) = -4(x² - 6x - 6x + 36) + 15

Combine like terms:

f(x) = -4(x² -12x + 36) + 15

Distribute -4 into the parenthesis:

f(x) = -4x² + 48x - 144 + 15

Combine the constants:

f(x) = -4x² + 48x - 129 ⇒ This is the quadratic function in standard form where a = -4, b = 48, and c = -129.