Graphing Parabolas Math Example 4

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Example 4

medium
The vertex of a parabola is (0,−4)(0, -4) and it passes through (2,0)(2, 0). Find the equation.

Solution

  1. 1
    Vertex form: f(x)=a(x−0)2+(−4)=ax2−4f(x) = a(x - 0)^2 + (-4) = ax^2 - 4.
  2. 2
    Use (2,0)(2, 0): 0=4a−40 = 4a - 4, so a=1a = 1. Equation: f(x)=x2−4f(x) = x^2 - 4.

Answer

f(x)=x2−4f(x) = x^2 - 4
Given the vertex and one point, use vertex form and solve for aa.

About Graphing Parabolas

The process of plotting a quadratic function by identifying its key features: vertex, axis of symmetry, direction of opening, yy-intercept, and xx-intercepts (if they exist).

Learn more about Graphing Parabolas →

More Graphing Parabolas Examples

Example 1 easy

Identify the key features of [formula] for graphing.

Example 2 medium

Sketch [formula]. Find vertex and intercepts.

Example 3 easy

Does [formula] have any [formula]-intercepts?

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