A table of values can be useful to identify coordinate pairs which satisfy the equation.
By substituting the values for x, you can calculate corresponding values for y.
If used correctly, your calculator can be a powerful tool to speed up calculations.

Common misconception

To draw a graph, points should always be joined with line segments.

For the graph of $$y=x^2$$ show the line joining $$(0,0)$$ and $$(1,1)$$ and ask pupils to test some coordinate pairs from that line in the original equation. For example, $$({1\over2},{1\over2})$$ does not satisfy the equation.

Keywords

Quadratic - A quadratic is an equation, graph, or sequence whereby the highest exponent of the variable is 2 The general form for a quadratic is $$ax2 + bx + c$$
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 (the directrix).

To obtain the smoothest parabola when drawing, a right-handed pupil may find it beneficial to draw the curve in the second quadrant with their page upright, then turn the page upside down to complete the graph in the first quadrant. The opposite applies for a left-handed pupil.

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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Starter quiz

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6 Questions

Q1.

$$x^2 + 5x - 7 = 0$$ is an example of a __________ equation.

Cubic

Linear

Correct answer: Quadratic

Q2.

In the equation $$y=x^2-5$$, what is the value of $$y$$ when $$x=4$$?

Correct Answer: 11, y=11

Q3.

In the equation $$y=x^2-5$$, what is the value of $$y$$ when $$x=-4$$?

$$21$$

Correct answer: $$11$$

$$-11$$

$$-21$$

Q4.

In the equation $$y=3-x^2$$, what is the value of $$y$$ when $$x=-2$$?

$$7$$

$$1$$

Correct answer: $$-1$$

$$-7$$

Q5.

In the equation $$y=4x^2$$, what is the value of $$y$$ when $$x=-5$$?

Correct Answer: 100, y=100

Q6.

In the equation $$y=x^2-5x-7$$, what is the value of $$y$$ when $$x=-2$$?

Correct Answer: 7, y=7

Exit quiz

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6 Questions

Q1.

The shape of the graph of a quadratic equation is called a .

Correct Answer: parabola, Parabola

Q2.

Some Oak pupils compare the graph of $$y=x^2$$ to the graph of $$y=x^2-6$$. Which of their statements are true?

Aisha: They will be different shapes.

Correct answer: Andeep: They will different $$y$$-intercepts.

Jacob: One parabola will be increasing, the other will be decreasing.

Correct answer: Sam: They will have the same shape; that of a parabola.

Q3.

Some Oak pupils compare the graph of $$y=8+x^2$$ to the graph of $$y=8-x^2$$. Which of their statements are true?

Correct answer: Jun: They will have a common $$y$$-intercept.

Laura: They will have the same $$x$$-intercepts.

Sam: They have same graph because squaring a negative gives a positive result.

Correct answer: Sofia: One parabola will minimum $$y$$ value, the other a maximum $$y$$ value.

Q4.

Which one of these coordinates do not satisfy the equation $$y=x^2-4x+8$$?

(-1, 13)

(0, 8)

(1, 5)

(2, 4)

Correct answer: (4, 3)

Q5.

Use a calculator to check this table of values for the equation $$y=3x^2-7x+1$$. Identify which coordinate pair is incorrect.

(-2, 27)

(-1, 11)

Correct answer: (2, 1)

(1, -3)

(3, 7)

Q6.

Identify the line of symmetry of the graph of the equation $$y=2x^2-6x+1$$.

$$x=0.5$$

$$x=1.25$$

Correct answer: $$x=1.5$$

$$x=2$$

$$x=2.5$$