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Drawing cubic graphs

I can generate coordinate pairs for a cubic graph from its equation and then draw the graph.

New
New

Drawing cubic graphs

I can generate coordinate pairs for a cubic graph from its equation and then draw the graph.

Lesson details

Key learning points

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

Keywords

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

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, $$(1/2,1/2)$$ does not satisfy the equation.

To obtain the smoothest parabola when drawing, a right-handed pupil may find it beneficial to draw the curve in the third quadrant with their page upright, then turn the page upside down to complete the graph in the first quadrant. The opposite applies for a left-handed pupil.
Teacher tip

Equipment

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Prior knowledge starter quiz

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6 Questions

Q1.
In the equation $$y=5x^3-7$$, the $$3$$ is the __________ of $$x$$.

base
coefficient
Correct answer: exponent
multiplier

Q2.
What is the value of $$x^3$$ when $$x=4$$?

7
12
16
Correct answer: 64

Q3.
What is the value of $$x^3$$ when $$x=-2$$?

Correct answer: -8
-6
1
6
8

Q4.
Match each $$x$$ value to its corresponding $$y$$ value for the equation $$y=x^3-2$$.

Correct Answer:$$x=-2$$,$$y=-10$$

$$y=-10$$

Correct Answer:$$x=-1$$,$$y=-3$$

$$y=-3$$

Correct Answer:$$x=0$$,$$y=-2$$

$$y=-2$$

Correct Answer:$$x=1$$,$$y=-1$$

$$y=-1$$

Correct Answer:$$x=2$$,$$y=6$$

$$y=6$$

Correct Answer:$$x=3$$,$$y=25$$

$$y=25$$

Q5.
Where is the $$y$$-intercept of the equation $$y=x^2-7x+8$$?

(0, -7)
(-7, 0)
Correct answer: (0, 8)
(8, 0)
(0, 1)

Q6.
Use a calculator to find the $$y$$ value when $$x=4$$ in the equation $$y=x^{3}-3x^{2}+2x$$.

Correct Answer: 24, y=24, y = 24, y= 24, y =24

Assessment exit quiz

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6 Questions

Q1.
$$y=x^3-7$$ is a __________ equation.

Correct answer: cubic
linear
quadratic
quartic

Q2.
Which $$y$$ value is incorrect in this table of values for the equation $$y=x^3-9$$? Use a calculator.

An image in a quiz
$$-17$$
$$-10$$
$$-9$$
$$-8$$
Correct answer: $$-7$$

Q3.
What is the $$y$$ value when $$x=-3$$ for the equation $$y=12-x^3$$? Do not use a calculator for this question.

Correct Answer: 39, y=39

Q4.
What is the general form for a cubic?

$$x^3$$
$$ax^3$$
$$x^3 + x^2 + x$$
Correct answer: $$ax^3 + bx^2 + cx + d$$
$$ax^3 + d$$

Q5.
The diagram shows the graph of a cubic of the form $$y=ax^3+d$$. Which of these statements are correct?

An image in a quiz
The constant term is positive.
Correct answer: The constant term is negative.
Correct answer: The coefficient of $$x^3$$ is positive.
The coefficient of $$x^3$$ is positive.

Q6.
Which of these will be $$y$$ values in this table for the equation $$x^{3}-5x^{2}+3x-4$$? Use a calculator.

An image in a quiz
Correct answer: $$-38$$
$$-30$$
Correct answer: $$-5$$
Correct answer: $$-10$$
$$-15$$

Lesson appears in

UnitMaths / Non-linear graphs

Maths

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