Quadratic Vertex Form Math Example 3

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

Example 3

easy
What is the vertex of g(x)=−(x+5)2−2g(x) = -(x + 5)^2 - 2?

Solution

  1. 1
    Rewrite as g(x)=−(x−(−5))2+(−2)g(x) = -(x - (-5))^2 + (-2).
  2. 2
    Vertex: (−5,−2)(-5, -2). The parabola opens downward (a=−1<0a = -1 < 0).

Answer

(−5,−2)(-5, -2)
Be careful with signs: (x+5)=(x−(−5))(x + 5) = (x - (-5)), so h=−5h = -5.

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 4 hard

Convert [formula] to vertex form.

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