icon-background-square
New
New
Year 10
Higher

Key features of a cubic graph

I can identify the key features of a cubic graph.

icon-background-square
New
New
Year 10
Higher

Key features of a cubic graph

I can identify the key features of a cubic graph.

warning

These resources will be removed by end of Summer Term 2025.

Switch to our new teaching resources now - designed by teachers and leading subject experts, and tested in classrooms.

Lesson details

Key learning points

  1. A cubic graph has a distinct shape.
  2. The roots of a cubic graph are where the graph intersects with the x-axis.
  3. The turning points are the local maximum and local minimum points of the graph.

Keywords

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

  • Roots - When drawing the graph of an equation, the roots of the equation are where its graph intercepts the x-axis (where y = 0).

  • Turning point - The turning point of a graph is a point on the curve where, as x increases, the y values change from decreasing to increasing or vice versa.

Common misconception

$$y=x^3$$ has one root so all cubic graphs have one root.

Make sure pupils see a wide variety of cubic graphs; ones with one root, two roots and three roots and link every one back to its equation and that the highest exponent of the variable is $$3$$ so they are all cubic graphs.

Have Desmos.com on a screen visible to pupils during the lesson and get them to suggest cubic equations to graph. Get pupils to pick out the key features of their equations.
speech-bubble
Teacher tip
copyright

Licence

This content is © Oak National Academy Limited (2024), licensed on

except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

Loading...

6 Questions

Q1.
A cubic is an equation, graph, or sequence where the highest __________ of the variable is 3.
base
coefficient
Correct answer: exponent
factor
multiple
Q2.
How many solutions can a quadratic equation have?
1
1 or 2
2
0 or 1
Correct answer: 0, 1 or 2
Q3.
What is $$y$$-intercept of this quadratic graph?
An image in a quiz
8
$$y$$ = 8
Correct answer: (0, 8)
(4, 0)
(2, 0)
Q4.
What are the roots of this quadratic equation?
An image in a quiz
(2, 0)
(4, 0)
Correct answer: $$x$$ = 2
Correct answer: $$x$$ = 4
$$y$$ = 8
Q5.
The point (3, -1) is the point of this quadratic curve.
An image in a quiz
Correct Answer: minimum, turning
Q6.
Factorise $$x^2-6x$$.
$$(x+1)(x-6)$$
$$(x-1)(x-6)$$
Correct answer: $$x(x-6)$$
$$(x-1)(x+6)$$
$$(x+1)(x+6)$$

6 Questions

Q1.
The point on the graph of a curve where, as $$x$$ increases, the $$y$$ values change from decreasing to increasing (or vice versa) is called the __________.
root
Correct answer: turning point
$$x$$-intercept
$$y$$-intercept
Q2.
How many roots can the graph of a cubic equation have?
1
3
1 or 3
Correct answer: 1, 2 or 3
0, 1, 2 or 3
Q3.
This is the graph of $$y=x^{3}-9x^{2}+24x-16$$. Which $$y$$ values make this statement true? $$y=x^{3}-9x^{2}+24x-16$$ has two solutions.
An image in a quiz
5
Correct answer: 4
2
Correct answer: 0
-3
Q4.
This is the equation $$y=x^{3}-9x^{2}+24x-16$$. The root $$x=4$$ is a __________.
An image in a quiz
Correct answer: repeated root
minimum value
Correct answer: turning point
Correct answer: local minimum
local maximum
Q5.
The equation $$y=x^3-21x+20$$ factorises to $$y=(x-1)(x-4)(x+5)$$. What are the roots of the equation?
Correct answer: $$x=1$$
Correct answer: $$x=4$$
$$x=-1$$
$$x=-4$$
Correct answer: $$x=-5$$
Q6.
$$x=-5$$ and $$x=0$$ are two roots of $$y=x^3+2x^2-15x$$. The third root is $$x=$$ .
Correct Answer: 3, x=3