Graph Features of a Parabola

Understanding parabola graph features

A parabola is the graph of a quadratic expression. These exercises ask you to identify and use key features of that graph, then give the final result in simplified form.

1) Read the important features

Look for the vertex, axis of symmetry, opening direction, and any intercepts if they are given or can be found. The vertex is the turning point. The axis of symmetry is the vertical line through the vertex. A positive leading coefficient means the parabola opens upward; a negative one means it opens downward.

2) Use the feature that matches the question

• If the vertex is given, use it directly.
• If the equation is in vertex form, identify the vertex from the expression.
• If intercepts are given, use them to locate points on the graph.
• If you need symmetry, remember points on one side of the axis match points the same distance on the other side.

3) Simplify carefully

Write coordinates in simplest form. Reduce fractions, combine like terms, and keep signs correct. If the question asks for a specific feature, answer only that feature.

4) Check your work

Make sure the point lies on the correct side of the axis, the opening direction matches the coefficient, and the vertex fits the graph shape. If you found a value from the equation, substitute it back to confirm it works.