Quadratic Vertex Form Math Example 4

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

Example 4

hard
Convert x2+4x+7x^2 + 4x + 7 to vertex form.

Solution

  1. 1
    Complete the square: x2+4x+4+3=(x+2)2+3x^2 + 4x + 4 + 3 = (x + 2)^2 + 3.
  2. 2
    Vertex form: (x+2)2+3(x + 2)^2 + 3, vertex at (−2,3)(-2, 3).

Answer

(x+2)2+3(x + 2)^2 + 3
Converting to vertex form requires completing the square. The vertex reveals the minimum value of the expression.

About Quadratic Vertex Form

A quadratic written as f(x)=a(x−h)2+kf(x) = a(x - h)^2 + k, where the vertex (h,k)(h, k) is directly readable from the formula.

Learn more about Quadratic Vertex Form →

More Quadratic Vertex Form Examples

Example 1 easy

What is the vertex of [formula]?

Example 2 medium

Write the vertex form of a parabola with vertex [formula] passing through [formula].

Example 3 easy

What is the vertex of [formula]?

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