Quadratic graphs might look intimidating, but they're actually quite straightforward... Show more
Maths69 views·Updated May 19, 2026·2 pagesUnderstanding Quadratics: Drawing Quadratic Graphs
J
Jessica Mcconville@jessicamcconville_aupp
1
of 2
Finding the Essential Points
Drawing quadratic graphs becomes much easier when you follow a systematic approach. You'll need to find four crucial elements: the roots, line of symmetry, turning point, and y-intercept.
Let's work through the example f(x) = x² + 2x - 8 step by step. First, find the roots by setting y = 0 and factorising. When you factorise x² + 2x - 8, you get = 0, giving you roots at x = -4 and x = 2.
Next, locate the line of symmetry by finding the midpoint between your roots. Simply add them together and divide by 2: (-4 + 2) ÷ 2 = -1. So your line of symmetry is x = -1.
Top Tip: The line of symmetry always passes through the turning point - this makes finding it much simpler!
2
of 2
Completing Your Graph
Now you can find the turning point easily since it sits on the line of symmetry at x = -1. Substitute this back into your equation: y = (-1)² + 2(-1) - 8 = -9. Your turning point is at (-1, -9).
For the y-intercept, simply set x = 0 in your equation. This gives you y = 0² + 2(0) - 8 = -8, so your y-intercept is at (0, -8).
You now have everything needed to sketch your graph: roots at (-4, 0) and (2, 0), turning point at (-1, -9), and y-intercept at (0, -8). Adding a couple of extra points like (-5, 7) and (3, 7) helps create that perfect U-shape.
Remember: Quadratic graphs are always symmetrical, so if you plot one side correctly, the other side mirrors it perfectly!
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Maths69 views·Updated May 19, 2026·2 pagesUnderstanding Quadratics: Drawing Quadratic Graphs
J
Jessica Mcconville@jessicamcconville_aupp
Quadratic graphs might look intimidating, but they're actually quite straightforward once you know the four key steps. These U-shaped curves pop up everywhere in maths, and mastering them will give you a solid foundation for A-levels and beyond.
1
of 2Sign up to see the content. It's free!
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Finding the Essential Points
Drawing quadratic graphs becomes much easier when you follow a systematic approach. You'll need to find four crucial elements: the roots, line of symmetry, turning point, and y-intercept.
Let's work through the example f(x) = x² + 2x - 8 step by step. First, find the roots by setting y = 0 and factorising. When you factorise x² + 2x - 8, you get = 0, giving you roots at x = -4 and x = 2.
Next, locate the line of symmetry by finding the midpoint between your roots. Simply add them together and divide by 2: (-4 + 2) ÷ 2 = -1. So your line of symmetry is x = -1.
Top Tip: The line of symmetry always passes through the turning point - this makes finding it much simpler!
2
of 2Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
Completing Your Graph
Now you can find the turning point easily since it sits on the line of symmetry at x = -1. Substitute this back into your equation: y = (-1)² + 2(-1) - 8 = -9. Your turning point is at (-1, -9).
For the y-intercept, simply set x = 0 in your equation. This gives you y = 0² + 2(0) - 8 = -8, so your y-intercept is at (0, -8).
You now have everything needed to sketch your graph: roots at (-4, 0) and (2, 0), turning point at (-1, -9), and y-intercept at (0, -8). Adding a couple of extra points like (-5, 7) and (3, 7) helps create that perfect U-shape.
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