Key features of a cubic graph | Maths | Quizalize & Oak National Academy

Starter quiz

A cubic is an equation, graph, or sequence where the highest __________ of the variable is 3.

base

coefficient

exponent ✓

factor

multiple
How many solutions can a quadratic equation have?

1

1 or 2

2

0 or 1

0, 1 or 2 ✓
What is $y$ -intercept of this quadratic graph?

8

$y$ = 8

(0, 8) ✓

(4, 0)

(2, 0)
What are the roots of this quadratic equation?

(2, 0)

(4, 0)

$x$ = 2 ✓

$x$ = 4 ✓

$y$ = 8
The point (3, -1) is the ______ point of this quadratic curve.

'minimum' ✓
Factorise $x^2-6x$ .

$(x+1)(x-6)$

$(x-1)(x-6)$

$x(x-6)$ ✓

$(x-1)(x+6)$

$(x+1)(x+6)$

Exit quiz

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

turning point ✓

$x$ -intercept

$y$ -intercept
How many roots can the graph of a cubic equation have?

1

3

1 or 3

1, 2 or 3 ✓

0, 1, 2 or 3
$This is the graph of <Math>y=x^{3}-9x^{2}+24x-16</Math>. Which <Math>y</Math> values make this statement true? <Math>y=x^{3}-9x^{2}+24x-16</Math> has two solutions.$

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.

5

4 ✓

2

0 ✓

-3
$This is the equation <Math>y=x^{3}-9x^{2}+24x-16</Math>. The root <Math>x=4</Math> is a __________.$

This is the equation $y=x^{3}-9x^{2}+24x-16$ . The root $x=4$ is a __________.

repeated root ✓

minimum value

turning point ✓

local minimum ✓

local maximum
The equation $y=x^3-21x+20$ factorises to $y=(x-1)(x-4)(x+5)$ . What are the roots of the equation?

$x=1$ ✓

$x=4$ ✓

$x=-1$

$x=-4$

$x=-5$ ✓
$x=-5$ and $x=0$ are two roots of $y=x^3+2x^2-15x$ . The third root is $x=$ ______.

'3' ✓

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Lesson Details

Key learning points

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

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.

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.