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

Ask pupils to verbalise their reasoning when matching graphs to equations. "How do you 'know' that is the graph of... ?" is a key question to ask once pupils have matched a pair. Being able to justify with technical vocabulary is a powerful skill in mathematics.

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Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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6 Questions

Q1.

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

Correct answer: $$y$$-intercept

$$y$$-intersection

$$y$$-axis

Q2.

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

curved

gradient

Correct answer: linear

parabolic

Q3.

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

Correct Answer: 16, y=16, y = 16

Q4.

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

Correct Answer: -8, y=-8, y = -8

Q5.

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

Correct answer: $$(2,{1\over2})$$

$$(1,-1)$$

$$(-1,1)$$

Correct answer: $$(-1,-1)$$

$$(-{1\over2},2)$$

Q6.

This graph represents __________ of distance with respect to time.

Correct answer: an increasing rate of change

a decreasing rate of change

a constant rate of change

Exit quiz

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6 Questions

Q1.

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

Correct answer: cubic curve

linear graph

parabola

reciprocal graph

Q2.

Which of these could be the equation of this graph?

Correct answer: $$-x^2+3$$

$$x^2+3$$

$$-x^2-3$$

$$x^2-3$$

$$x^3+3$$

Q3.

Which of these could be the equation of this graph?

Correct answer: $$x^2-5$$

$$x^2+5$$

$$-x^2+5$$

$$-x^2-5$$

$$2x-5$$

Q4.

Which of these could be the equation of this graph?

$$y=x^3$$

$$y=-x^3$$

Correct answer: $$y=x^3-2$$

$$y=x^3+2$$

$$y=x^2-3$$

Q5.

Which of these equations could this graph represent?

Correct answer: $$y={5\over{x}}$$

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

$$y=x^3$$

Correct answer: $$y={3\over{x}}$$

$$y={-3\over{x}}$$

Q6.

Given that water is added at a steady rate which vase would generate this Depth-Time graph?

Correct answer: a