Quadratic Vertex Form Math Example 2

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Example 2

medium
Write the vertex form of a parabola with vertex (−1,4)(-1, 4) passing through (0,7)(0, 7).

Solution

  1. 1
    Start with f(x)=a(x−(−1))2+4=a(x+1)2+4f(x) = a(x - (-1))^2 + 4 = a(x+1)^2 + 4.
  2. 2
    Use the point (0,7)(0, 7): 7=a(0+1)2+4=a+47 = a(0+1)^2 + 4 = a + 4.
  3. 3
    Solve: a=3a = 3. The equation is f(x)=3(x+1)2+4f(x) = 3(x+1)^2 + 4.

Answer

f(x)=3(x+1)2+4f(x) = 3(x+1)^2 + 4
Given the vertex, write the general vertex form and use another point to find the value of aa.

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 3 easy

What is the vertex of [formula]?

Example 4 hard

Convert [formula] to vertex form.

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