New
New
Year 9

Exploring the shapes of graphs using technology

I can appreciate that different types of equations give rise to different graph shapes, identifying quadratics in particular.

New
New
Year 9

Exploring the shapes of graphs using technology

I can appreciate that different types of equations give rise to different graph shapes, identifying quadratics in particular.

Lesson details

Key learning points

  1. There are many different types of equations.
  2. You can plot the graph of an equation if you have two variables (one for each axis).
  3. Certain types of equation give rise to certain graph shapes.
  4. Linear equations produce a straight line.
  5. 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).

Ask pupils to use precise language to describe graphs. "What kind of graph does that equation make?" should be answered with, "A linear graph", "A parabola", or "A cubic curve".
Teacher tip

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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6 Questions

Q1.
The linear equation $$y=3x-7$$ will form a __________ graph.
curved
Correct answer: decreasing
straight line
Q2.
Which of these coordinates will be on the linear graph $$y=3x-7$$?
Correct answer: (5, 8)
(8,5)
(-4, -1)
Correct answer: (1, -4)
Correct answer: (2, -1)
Q3.
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.
Correct answer: The number of points you can plot on this graph goes on infinitely.
Q4.
If you were populating this table of values for the linear equation $$y=8-5x$$, what is highest value of $$y$$ you will get?
An image in a quiz
3
5
8
Correct answer: 23
28
Q5.
If you were populating this table of values for the linear equation $$y=8-5x$$, what is lowest value of $$y$$ you will get?
An image in a quiz
23
-3
-5
Correct answer: -7
-23
Q6.
Which of these equation will produce a non-linear graph?
$$y=3x+8$$
$$y=3x-8$$
$$y=8-3x$$
$$3x+y=8$$
Correct answer: $$y=x^3+8$$

6 Questions

Q1.
A __________ equation is an equation where the highest exponent of the variable is 2.
arithmetic
cubic
geometric
linear
Correct answer: quadratic
Q2.
Select all the quadratic equations.
$$y=x+2$$
$$y=2x$$
Correct answer: $$y=x^2$$
Correct answer: $$y=x^2+3x$$
$$y=x^2+x^3$$
Q3.
__________ is a special symmetrical curve which can be bowl-shaped or archlike.
A cubic curve
An exponent
A straight-line
Correct answer: A parabola
A parallel
Q4.
Which of the below equations will form a parabola when plotted?
Correct answer: $$y=x^2$$
Correct answer: $$y=x^2+3x$$
$$x+y=2$$
Correct answer: $$y=-x^2$$
$$y=x^3+x^2$$
Q5.
Match each equation to the description of its shape when graphed.
Correct Answer:$$2x+3y=12$$,Straight graph.

Straight graph.

Correct Answer:$$y=x^2+3x$$,Parabola.

Parabola.

Correct Answer:$$y=x^3+2x$$,Cubic curve.

Cubic curve.

Q6.
Which of these equations will produce parabolas that are 'archlike' or appear to 'open downwards' when graphed?
$$y=x^2-5$$
$$y=x^2-5x$$
$$y=x^2+5x$$
Correct answer: $$y=5-x^2$$
$$y=5+x^2$$