Exploring the shapes of graphs using technology | Maths

Starter quiz

The linear equation $y=3x-7$ will form a __________ graph.

curved

decreasing ✓

straight line
Which of these coordinates will be on the linear graph $y=3x-7$ ?

(5, 8) ✓

(8,5)

(-4, -1)

(1, -4) ✓

(2, -1) ✓
How many points can be plotted on the graph of the linear equation $y=3x-7$ ?

All integers.

Positive integer values only.

Negative integer values only.

Millions but, there is a limit.

The number of points you can plot on this graph goes on infinitely. ✓
If you were populating this table of values for the linear equation $y=8-5x$ , what is highest value of $y$ you will get?

3

5

8

23 ✓

28
If you were populating this table of values for the linear equation $y=8-5x$ , what is lowest value of $y$ you will get?

23

-3

-5

-7 ✓

-23
Which of these equation will produce a non-linear graph?

$y=3x+8$

$y=3x-8$

$y=8-3x$

$3x+y=8$

$y=x^3+8$ ✓

Exit quiz

A __________ equation is an equation where the highest exponent of the variable is 2.

arithmetic

cubic

geometric

linear

quadratic ✓
Select all the quadratic equations.

$y=x+2$

$y=2x$

$y=x^2$ ✓

$y=x^2+3x$ ✓

$y=x^2+x^3$
__________ is a special symmetrical curve which can be bowl-shaped or archlike.

A cubic curve

An exponent

A straight-line

A parabola ✓

A parallel
Which of the below equations will form a parabola when plotted?

$y=x^2$ ✓

$y=x^2+3x$ ✓

$x+y=2$

$y=-x^2$ ✓

$y=x^3+x^2$
Match each equation to the description of its shape when graphed.

$2x+3y=12$

⇔

Straight graph. ✓

$y=x^2+3x$

⇔

Parabola. ✓

$y=x^3+2x$

⇔

Cubic curve. ✓
Which of these equations will produce parabolas that are 'archlike' or appear to 'open downwards' when graphed?

$y=x^2-5$

$y=x^2-5x$

$y=x^2+5x$

$y=5-x^2$ ✓

$y=5+x^2$

Worksheet

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Lesson Details

Key learning points

There are many different types of equations.
You can plot the graph of an equation if you have two variables (one for each axis).
Certain types of equation give rise to certain graph shapes.
Linear equations produce a straight line.
Quadratic equations produce a parabola.

Common misconception

After plotting the integer coordinate pairs of a quadratic, they should be joined with a straight line.

Use graphing technology to plot coordinate pairs that use smaller and smaller non-integer steps between $x$ -coordinates. This will reveal the true, curved nature of the line.

Keywords

Quadratic - A quadratic is an equation whereby the highest exponent of the variable is 2; the graph of which forms a parabola.
Parabola - A parabola is a curve where any point on the curve is an equal distance from a fixed point (the focus) and a fixed straight line (a directrix).