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Year 9 · Non-linear graphs
Substitute values into an expression with a squared term
Definition
A graph turns an equation into a picture. Straight-line graphs come from equations like y = 2x + 1; quadratic equations like y = x² draw a smooth U-shaped curve called a parabola.
Why Do I Have to Learn This?
Quadratics describe curves like the path of a thrown ball. Their graphs help us find the highest point, and where things land.
Key Rules:
- 1. In y = mx + c, m is the gradient (steepness) and c is where it crosses the y-axis.
- 2. A quadratic has an x² term and makes a symmetrical parabola.
- 3. Where a curve crosses the x-axis are its roots (solutions).
Remember:
- •A bigger number in front of x² makes the parabola narrower, not taller-only.
- •A negative x² coefficient flips the U upside-down.
- •Plot several points and join with a smooth curve, not straight segments.
Gradient
How steep a line is: how far it rises for each step across. Gradient = change in y ÷ change in x.
A line that goes up 6 for every 2 across has a gradient of 3.
Animated Example:
y = 1x²
Free Substitute values into an expression with a squared term Worksheet
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Let’s Practise the Concept
Step 1 of 3
Solve it
5x + 9 = 34. What is x?