Quadratic Graphs
The graph of a quadratic is a smooth symmetric curve called a parabola that opens up or down depending on the sign of a.
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The graph of a quadratic is a smooth symmetric curve called a parabola that opens up or down depending on the sign of a.
- Positive a gives a U shape
- The axis of symmetry passes through the vertex
- The y-intercept equals c
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Quadratic Graphs?
Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Quadratic Graphs. Maths builds step by step, so each topic here gives you a rule, a picture and a quick check you can use on homework and in exams.
Check that you can explain Quadratic Graphs in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Quadratic Graphs gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
Quadratic Graphs in detail
The graph of y = ax² + bx + c is a smooth, symmetrical U-shaped curve called a parabola. If a is positive it opens upwards with a minimum point, and if a is negative it opens downwards with a maximum. The line of symmetry passes through the turning point.
Key features are the roots where it crosses the x-axis, the y-intercept at c and the turning point, found by completing the square or using symmetry halfway between the roots. Quadratic graphs model the path of a thrown ball, the shape of bridges and satellite dishes, and profit problems.
How the interactive helps you understand Quadratic Graphs
Move the sliders to change the values in the equation. The curve, the moving point and, where they exist, the roots (the points where the curve crosses the x-axis) update straight away.
Before you change anything, predict the result. Then change one value at a time and check whether your prediction was right. This is a quick way to build a correct mental model of Quadratic Graphs.
Real-life uses and examples
- Explain Quadratic Graphs to a friend with a simple picture, such as a row of tiles or a bag of sweets.
- Spot Quadratic Graphs in exam questions, where it often sits inside a short word problem.
- Check a homework answer about Quadratic Graphs by estimating first, then working it out step by step.
Common mistakes to avoid
- Memorising the steps for Quadratic Graphs without checking why they work.
- Forgetting units, signs or brackets when you apply Quadratic Graphs.
- Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.
Frequently asked questions about Quadratic Graphs
What is Quadratic Graphs?
The graph of a quadratic is a smooth symmetric curve called a parabola that opens up or down depending on the sign of a.
What are the most important points about Quadratic Graphs?
The main points are: Positive a gives a U shape; The axis of symmetry passes through the vertex; The y-intercept equals c.
Why is Quadratic Graphs useful?
Understanding Quadratic Graphs gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
How can I practise Quadratic Graphs?
Open the interactive at the top of this page and change the controls one at a time. Predict the result before each change, then take the three-question quiz. A score of two or more marks the topic as complete on this device.
Which topics are related to Quadratic Graphs?
Related topics in Mathematics include Transformations of Graphs, Functions, Angles in Parallel Lines.