Practice Graphing Parabolas in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

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

A parabola is a U-shaped curve (or upside-down U). Start by finding the vertex—that is the turning point. Then the axis of symmetry tells you the curve is a mirror image on both sides. Plot a few symmetric points and connect them in a smooth curve.

Example 1

easy
Identify the key features of f(x) = x^2 - 4x + 3 for graphing.

Example 2

medium
Sketch g(x) = -x^2 + 2x + 3. Find vertex and intercepts.

Example 3

easy
Does f(x) = 5x^2 + 1 have any x-intercepts?

Example 4

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