Checking and securing understanding of drawing quadratic graphs | Maths

Starter quiz

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

Cubic

Linear

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

'11' ✓
In the equation $y=x^2-5$ , what is the value of $y$ when $x=-4$ ?

$21$

$11$ ✓

$-11$

$-21$
In the equation $y=3-x^2$ , what is the value of $y$ when $x=-2$ ?

$7$

$1$

$-1$ ✓

$-7$
In the equation $y=4x^2$ , what is the value of $y$ when $x=-5$ ? ______

'100' ✓
In the equation $y=x^2-5x-7$ , what is the value of $y$ when $x=-2$ ?

'7' ✓

Exit quiz

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

'parabola' ✓
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.

Andeep: They will different $y$ -intercepts. ✓

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

Sam: They will have the same shape; that of a parabola. ✓
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?

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.

Sofia: One parabola will minimum $y$ value, the other a maximum $y$ value. ✓
Which one of these coordinates do not satisfy the equation $y=x^2-4x+8$ ?

(-1, 13)

(0, 8)

(1, 5)

(2, 4)

(4, 3) ✓
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)

(2, 1) ✓

(1, -3)

(3, 7)
Identify the line of symmetry of the graph of the equation $y=2x^2-6x+1$ .

$x=0.5$

$x=1.25$

$x=1.5$ ✓

$x=2$

$x=2.5$

Worksheet

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Lesson Details

Key learning points

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).