Completing the Square Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

medium
Rewrite x2−8x+20x^2 - 8x + 20 in vertex form.

Solution

  1. 1
    Half of −8-8 is −4-4; (−4)2=16(-4)^2 = 16.
  2. 2
    x2−8x+16+4=(x−4)2+4x^2 - 8x + 16 + 4 = (x - 4)^2 + 4.

Answer

(x−4)2+4(x - 4)^2 + 4
Vertex form reveals the vertex directly: (4,4)(4, 4). The minimum value of this expression is 4.

About Completing the Square

A technique for rewriting ax2+bx+cax^2 + bx + c in vertex form a(x−h)2+ka(x - h)^2 + k by adding and subtracting the value (b2a)2\left(\frac{b}{2a}\right)^2 to create a perfect square trinomial.

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More Completing the Square Examples

Example 1 medium

Rewrite [formula] in vertex form by completing the square.

Example 2 hard

Solve [formula] by completing the square.

Example 3 easy

What number completes the square for [formula]?

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