Plotting quadratic graphs

The Maths Habit

Sam says (−3)2 = −9. Is Sam right?

No: −3 × −3 = 9

Work out y

  1. y = x2 − 4 when x = 3

    y = 5

  2. y = x2 − 4 when x = −3

    y = 5

  3. y = 5 − x2 when x = −3

    5 − 9 = −4

Quadratic
An expression where the highest power of x is x2.
Parabola
The U shaped curve of a quadratic graph.

Straight lines or a smooth curve?

Joining the points of a quadratic graph A smooth curve

Complete the table for y = x2 + 3 and draw the graph.

x−3−2−10123
y127434712
Lowest point(0, 3)

Complete the table for y = x2 − 3 and draw the graph.

x−3−2−10123
y61−2−3−216
Lowest point(0, −3)

Complete the table for y = x2 + 3 and draw the graph.

x−3−2−10123
y127434712
Lowest point(0, 3)

Complete the table for y = x2 + 2x − 1 and draw the graph.

x−4−3−2−1012
y72−1−2−127
Lowest point(−1, −2)

Complete the table for y = x2 + 3 and draw the graph.

x−3−2−10123
y127434712
Lowest point(0, 3)

Complete the table for y = x2 − 4x + 2 and draw the graph.

x−1012345
y72−1−2−127
Lowest point(2, −2)

Complete the table for y = x2 + 3 and draw the graph.

x−3−2−10123
y127434712
Lowest point(0, 3)

Complete the table for y = x2 − 6x + 10 and draw the graph.

x0123456
y105212510
Lowest point(3, 1)

Complete the table for y = x2 + 3 and draw the graph.

x−3−2−10123
y127434712
Lowest point(0, 3)

Complete the table for y = x2 + 6x + 5 and draw the graph.

x−6−5−4−3−2−10
y50−3−4−305
Lowest point(−3, −4)

Plotting quadratic graphs worksheet, page 1

Answer sheet

  1. The graph of y = x2 − 4 crosses the x axis twice. Where?

    x = 2 and x = −2

  2. Sam plots y = x2 + 1 and gets y = −8 when x = −3. What has gone wrong?

    (−3)² is 9, so it is 10

  1. Complete the table of values for y = x2 − 2x − 3.

    0, −3, −4, −3, 0
    xy−10123

  2. Draw the graph of y = x2 − 2x − 3.

    Smooth curve, lowest (1, −4)
    xy−10123−4−3−2−101

  3. y = 10 − x2. Find y when x = −4.

    y = −6
Exit tickets to print