Question

Max rewrote the function f(x) = 4x² + 16x + 8 in vertex form by completing the square.

He concluded that the vertex is (-2, 4), which was incorrect. Consider Max's work, listed below.

In which step did Max make a mistake?

Step 1: f(x) = 4x² + 16x + 8

Step 2: f(x) = 4(x² + 4x) +8

Step 3: f(x) = 4(x² + 4x + 4) +8-4

Step 4: f(x) = 4(x + 2)² +4

Answer 1

The quadratic function f(x) = 4x² + 16x + 8 can be expressed in vertex form

Max's error is in step 3

How to determine the error in the function?

The function is given as:

$f(x) = 4x^2 + 16x + 8$

Factor out 4

$f(x) = 4(x^2 + 4x) + 8$

Take the coefficient of x

$k = 4$

Divide by 2

$k/2 = 2$

Square both sides

$(k/2)^2 = 4$

Add and subtract 4 to the bracket

$f(x) = 4(x^2 + 4x + 4 - 4) + 8$

Expand

$f(x) = 4(x^2 + 4x + 4) + 8 - 16$

By comparing the above equation to step 3 of Max solution, we can determine that Max's error is in step 3

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