Drawing cubic graphs | Maths | Quizalize & Oak National Academy

Starter quiz

In the equation $y=5x^3-7$ , the $3$ is the __________ of $x$ .

base

coefficient

exponent ✓

multiplier
What is the value of $x^3$ when $x=4$ ?

7

12

16

64 ✓
What is the value of $x^3$ when $x=-2$ ?

-8 ✓

-6

1

6

8
Match each $x$ value to its corresponding $y$ value for the equation $y=x^3-2$ .

$x=-2$

⇔

$y=-10$ ✓

$x=-1$

⇔

$y=-3$ ✓

$x=0$

⇔

$y=-2$ ✓

$x=1$

⇔

$y=-1$ ✓

$x=2$

⇔

$y=6$ ✓

$x=3$

⇔

$y=25$ ✓
Where is the $y$ -intercept of the equation $y=x^2-7x+8$ ?

(0, -7)

(-7, 0)

(0, 8) ✓

(8, 0)

(0, 1)
Use a calculator to find the $y$ value when $x=4$ in the equation $y=x^{3}-3x^{2}+2x$ .

'24' ✓

Exit quiz

$y=x^3-7$ is a __________ equation.

cubic ✓

linear

quadratic

quartic
Which $y$ value is incorrect in this table of values for the equation $y=x^3-9$ ? Use a calculator.

$-17$

$-10$

$-9$

$-8$

$-7$ ✓
What is the $y$ value when $x=-3$ for the equation $y=12-x^3$ ? Do not use a calculator for this question.

'39' ✓
What is the general form for a cubic?

$x^3$

$ax^3$

$x^3 + x^2 + x$

$ax^3 + bx^2 + cx + d$ ✓

$ax^3 + d$
The diagram shows the graph of a cubic of the form $y=ax^3+d$ . Which of these statements are correct?

The constant term is positive.

The constant term is negative. ✓

The coefficient of $x^3$ is positive. ✓

The coefficient of $x^3$ is positive. ✓
$Which of these will be <Math>y</Math> values in this table for the equation <Math>x^{3}-5x^{2}+3x-4</Math>? Use a calculator.$

Which of these will be $y$ values in this table for the equation $x^{3}-5x^{2}+3x-4$ ? Use a calculator.

$-38$ ✓

$-30$

$-5$ ✓

$-10$ ✓

$-15$

Worksheet

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Presentation

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Video

Lesson Details

Key learning points

A table of values can be useful to identify coordinate pairs which satisfy the equation.
By substituting the values for x, you can calculate corresponding values for y.
If used correctly, your calculator can be a powerful tool to speed up calculations.

Common misconception

To draw a graph, points should always be joined with line segments.

For the graph of $y=x^3$ show the line joining $(0,0)$ and $(1,1)$ and ask pupils to test some coordinate pairs from that line in the original equation. For example, $({1\\over2},{1\\over2})$ does not satisfy the equation.

Keywords

Cubic - A cubic is an equation, graph, or sequence whereby the highest exponent of the variable is 3