Drawing Quadratic Graphs worksheet

10 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.

10 questions 30 marks Sheet 1

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3 marks
The graph of \(y = x^2 - 6x + 5\) is drawn on the grid.

(a)
Write down the two values of \(x\) where the curve crosses the \(x\)-axis.

(b)
Write down the coordinates of the point where the curve crosses the \(y\)-axis.
3 marks The table shows some values of \(y = x^2 + 2x \)

x -4 -3 -2 -1 0 1 2

y 3 0 -1 0 8

Two of the \(y\) values are missing.
(a)
Work out the value of \(y\) when \(x = -4\).

(b)
Work out the value of \(y\) when \(x = 1\).

(c)
Write down the coordinates of the lowest point shown in the table.
2 marks
The graph of \(y = x^2 - 2x \) is drawn on the grid.

(a)
Write down the coordinates of the turning point of the curve.

(b)
Write down the equation of the line of symmetry of the curve.
3 marks
The graph of \(y = x^2 - 8x + 7\) is drawn on the grid.

(a)
Use the graph to write down the value of \(y\) when \(x = 3\).

(b)
Use the graph to write down the two values of \(x\) when \(y = -5\).
2 marks A student has filled in a table of values for \(y = x^2 - 4x \)

x -1 0 1 2 3 4 5

y 5 0 -3 -4 -2 0 5

One of the \(y\) values is wrong.
(a)
Write down the value of \(x\) for the entry that is wrong.

(b)
State the correct value of \(y\) for that entry.
2 marks
The graph of \(y = x^2 - 4x + 3\) and the line \(y = 3\) are both drawn on the grid.

Use the graphs to solve \(x^2 - 4x + 3 = 3\)
3 marks
The graph of \(y = -x^2 + 6x - 5\) is drawn on the grid.

Because of the minus sign in front of the \(x^2\), this parabola opens downwards.

(a)
Write down the coordinates of the highest point of the curve.

(b)
Write down the two values of \(x\) where the curve crosses the \(x\)-axis.
5 marks
A curve has equation \(y = (x + 9)(x + 3)\)

It is a parabola, and it opens upwards.

(a)
Write down the two values of \(x\) where the curve crosses the \(x\)-axis.

(b)
Write down the equation of the line of symmetry of the curve.

(c)
Work out the minimum value of \(y\).
4 marks
The graph of \(y = x^2 - 6x \) is drawn on the grid.

You are going to use it to solve \(x^2 - 6x + 5 = 0\)

(a)
Write down the equation of the straight line you should draw on the grid.

(b)
Use your line to solve \(x^2 - 6x + 5 = 0\)
3 marks
The graph of \(y = x^2 - 2x - 3\) is drawn on the grid.

(a)
Write down the two values of \(x\) where the curve crosses the \(x\)-axis.

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

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

x	-1	0	1	2	3	4	5
y	5	0	-3	-4	-2	0	5

Answers

(a) \(x = 1\) and \(x = 5\)
(b) \((0, 5)\)
(a) \(8\)
(b) \(3\)
(c) \((-1, -1)\)
(a) \((1, -1)\)
(b) \(x = 1\)
(a) \(-8\)
(b) \(x = 2\) and \(x = 6\)
(a) \(3\)
(b) \(-3\)
\(x = 0\) and \(x = 4\)
(a) \((3, 4)\)
(b) \(x = 1\) and \(x = 5\)
(a) \(x = -9\) and \(x = -3\)
(b) \(x = -6\)
(c) \(-9\)
(a) \(y = -5\)
(b) \(x = 1\) and \(x = 5\)
(a) \(x = -1\) and \(x = 3\)
(b) \((0, -3)\)

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