Problem solving with non-linear graphs | Maths | Quizalize & Oak National Academy

Starter quiz

For this linear graph $y=4x-3$ , the coordinates (0, -3) is the __________.

$y$ -intercept ✓

$y$ -intersection

$y$ -axis
$y=4x-3$ is a linear equation which therefore forms a __________ graph.

curved

gradient

linear ✓

parabolic
Izzy plots the graph of $y=x^2$ . When the $x$ coordinate is $-4$ , the $y$ coordinate is ______.

'16' ✓
Jacob plots the graph of $y=x^3$ . When the $x$ coordinate is $-2$ , the $y$ coordinate is ______.

'-8' ✓
Sofia plots the reciprocal graph $y={1\over{x}}$ . Which of these will be coordinate pairs?

$(2,{1\over2})$ ✓

$(1,-1)$

$(-1,1)$

$(-1,-1)$ ✓

$(-{1\over2},2)$
This graph represents __________ of distance with respect to time.

an increasing rate of change ✓

a decreasing rate of change

a constant rate of change

Exit quiz

The graph of $y=x^3+2$ will form a __________.

cubic curve ✓

linear graph

parabola

reciprocal graph
Which of these could be the equation of this graph?

$-x^2+3$ ✓

$x^2+3$

$-x^2-3$

$x^2-3$

$x^3+3$
Which of these could be the equation of this graph?

$x^2-5$ ✓

$x^2+5$

$-x^2+5$

$-x^2-5$

$2x-5$
Which of these could be the equation of this graph?

$y=x^3$

$y=-x^3$

$y=x^3-2$ ✓

$y=x^3+2$

$y=x^2-3$
Which of these equations could this graph represent?

$y={5\over{x}}$ ✓

$y={-5\over{x}}$

$y=x^3$

$y={3\over{x}}$ ✓

$y={-3\over{x}}$
Given that water is added at a steady rate which vase would generate this Depth-Time graph?

a ✓

b

c

d

Worksheet

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Lesson Details

Key learning points

The shape of the graph can be used to identify the form of its equation.
If the graph has a context, then the solutions should be given in context.

Common misconception

A graph drawn on axes with no scale shown means nothing is known about the graph.

Understanding the shape of a parabola, cubic curve, and reciprocal graph and then applying key features like positive/negative coefficients and $y$ -intercepts enables pupils to infer much about the equation without needing actual coordinate values.

Keywords

Linear - The relationship between two variables is linear if, when plotted on a pair of axes, a straight line is formed.
Quadratic - A quadratic is an equation, graph, or sequence whereby the highest exponent of the variable is 2
Cubic - A cubic is an equation, graph, or sequence whereby the highest exponent of the variable is 3