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
The curve $y = (x - 2)(x + 4)$ is to be sketched.

(a) Write down the coordinates of the points where the curve crosses the $x$ -axis. [1]

(b) Write down the coordinates of the point where the curve crosses the $y$ -axis. [1]

(c) Work out the coordinates of the turning point of the curve. [2]
Level 3 · 4 marksTry it
2
(a) Complete the table of values for $y = x^2 + 3x - 1$
$x$ $-4$ $-3$ $-2$ $-1$ $0$ $1$
$y$ $3$ $-1$ $3$
(2 marks)
(b) On the grid, draw the graph of $y = x^2 + 3x - 1$ for values of $x$ from $-4$ to $1$ (2 marks)
(c) Write down the coordinates of the turning point of the graph of $y = x^2 + 3x - 1$

(1 mark)
Level 3 · 5 marksTry it
3
(a) Complete the table of values for $y = x^2 - 2x - 8$
$x$ $-2$ $-1$ $0$ $1$ $2$ $3$ $4$
$y$ $0$ $-8$ $-8$ $0$
(b) Write down the coordinates of the turning point of the graph of $y = x^2 - 2x - 8$
Level 3 · 3 marksTry it
4
The diagram shows the graph of $y = x^2 - 4x + 3$ (a) Write down the roots of $x^2 - 4x + 3 = 0$

(b) Write down the coordinates of the turning point of the graph.
Level 3 · 2 marksTry it
5
The diagram shows the graph of $y = x^2 + 2x - 3$ (a) Write down the roots of $x^2 + 2x - 3 = 0$

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

(c) Write down the equation of the graph's line of symmetry.
Level 3 · 3 marksTry it

$x$	$-4$	$-3$	$-2$	$-1$	$0$	$1$
$y$	$3$				$-1$	$3$

$x$	$-2$	$-1$	$0$	$1$	$2$	$3$	$4$
$y$	$0$		$-8$		$-8$		$0$

1 more question on quadratic graphs

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