GCSE · Graphs of functions

Quadratic graphsExam-style questions

Why a quadratic draws a symmetric parabola, what the roots, y-intercept and turning point each are on the picture, and how the graph solves equations by intersection.

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14 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
A parabola crosses the $x$ -axis at $x = -1$ and $x = 5$ .

Find the equation of its line of symmetry.
Level 4 · 2 marksTry it
2
A curve has equation $y = (x - 2)(x + 4)$

(a) Write down the roots of $(x - 2)(x + 4) = 0$

(b) Write down the coordinates of the point where the curve crosses the $y$ -axis.

(c) Find the coordinates of the turning point of the curve.
Level 4 · 4 marksTry it
3
A parabola has line of symmetry $x = 3$ , and one of its roots is $x = -1$ .

(a) Find the other root.

(b) Write down the $x$ -coordinate of the parabola's turning point.
Level 4 · 3 marksTry it
4
A curve has equation $y = x^2 - 6x + 5$

(a) Factorise $x^2 - 6x + 5$

(b) Hence write down the roots of $x^2 - 6x + 5 = 0$

(c) Work out the coordinates of the curve's turning point.
Level 4 · 4 marksTry it