Plotting quadratic graphs

The Maths Habit

The same crosses are joined in two ways. Which is better?

A
B
B. The crosses curve. A has corners that are not really there.

Write the coordinates of P.123451234560xyP(2, 4)
What is 32?32
6932
9, because 32 means 3 × 3

Square
Multiply a number by itself.
xy
Table of values
A table of x values and the y value that goes with each one.
123412340xy
Plot
Mark a point on a grid with a cross.
123412340xy
Quadratic graph
A graph with x2 in its rule. It is a smooth curve.

Draw the graph of y = x2 + 2.

x0123y236111234246810121416180xy
1Work out each y.
2Plot each point.
3Join with a smooth curve.
(0, 2)(1, 3)(2, 6)(3, 11)

Draw the graph of y = x2 + 6.

x0123y6710151234246810121416180xy
1Work out each y.
2Plot each point.
3Join with a smooth curve.
(0, 6)(1, 7)(2, 10)(3, 15)

Draw the graph of y = x2 + 2.

x0123y236111234246810121416180xy
1Work out each y.
2Plot each point.
3Join with a smooth curve.
(0, 2)(1, 3)(2, 6)(3, 11)
1Work out each y.
2Plot each point.
3Join with a smooth curve.

Draw the graph of y = x2 + 8.

x0123y8912171234246810121416180xy
(0, 8)(1, 9)(2, 12)(3, 17)

Draw the graph of y = x2 + 2.

x0123y236111234246810121416180xy
1Work out each y.
2Plot each point.
3Join with a smooth curve.
(0, 2)(1, 3)(2, 6)(3, 11)
1Work out each y.
2Plot each point.
3Join with a smooth curve.

Draw the graph of y = x2 + 3.

x123y47121234246810121416180xy
(1, 4)(2, 7)(3, 12)

Draw the graph of y = x2 + 2.

x0123y236111234246810121416180xy
1Work out each y.
2Plot each point.
3Join with a smooth curve.
(0, 2)(1, 3)(2, 6)(3, 11)
1Work out each y.
2Plot each point.
3Join with a smooth curve.

Draw the graph of y = x2.

x0123y1234246810121416180xy0149
(0, 0)(1, 1)(2, 4)(3, 9)

x = 4. What is x2 + 3?

x2 + 3
111949
19. Square first: 4 × 4 = 16. Then add 3.

Draw the graph of y = x2 + 5.

x123x2 y1234246810121416180xy1496914
1Work out each y.
2Plot each point.
3Join with a smooth curve.
(1, 6)(2, 9)(3, 14)

Draw the graph of y = x2 + 8.

x012x2 014y1234246810121416180xy8912
1Work out each y.
2Plot each point.
3Join with a smooth curve.
(0, 8)(1, 9)(2, 12)

Draw the graph of y = x2 + 5.

x123x2 y1234246810121416180xy1496914
1Work out each y.
2Plot each point.
3Join with a smooth curve.
(1, 6)(2, 9)(3, 14)
1Work out each y.
2Plot each point.
3Join with a smooth curve.

Draw the graph of y = x2 + 1.

x234x2 4916y1234246810121416180xy51017
(2, 5)(3, 10)(4, 17)

Draw the graph of y = x2 + 5.

x123x2 y1234246810121416180xy1496914
1Work out each y.
2Plot each point.
3Join with a smooth curve.
(1, 6)(2, 9)(3, 14)
1Work out each y.
2Plot each point.
3Join with a smooth curve.

Draw the graph of y = x2 + 9.

x123x2 149y1234246810121416180xy101318
(1, 10)(2, 13)(3, 18)

Draw the graph of y = x2 + 5.

x123x2 y1234246810121416180xy1496914
1Work out each y.
2Plot each point.
3Join with a smooth curve.
(1, 6)(2, 9)(3, 14)
1Work out each y.
2Plot each point.
3Join with a smooth curve.

Draw the graph of y = x2 + 2.

x012x2 y1234246810121416180xy014236
(0, 2)(1, 3)(2, 6)

Thumbs up for yes. Thumbs down for no.

  1. Is (3, 10) on the curve y = x2 + 1?

    Yes

  2. Is (2, 4) on the curve y = x2 + 2?

    No: when x = 2, y = 6

  3. Is (4, 16) on the curve y = x2?

    Yes

  4. Is (3, 6) on the curve y = x2?

    No: when x = 3, y = 9

  5. Is (1, 6) on the curve y = x2 + 5?

    Yes

Plotting quadratic graphs worksheet, page 1

Plotting quadratic graphs worksheet, page 2

Answer sheet

  1. y = x2. Work out y when x = −3.

    y = 9

  2. Is the point (5, 25) on the curve y = x2? How do you know?

    Yes: 5 × 5 = 25

  3. y = x2 + 3. Which positive value of x gives y = 19?

    x = 4

  4. Does the curve y = 10 − x2 go up or down from x = 0 to x = 3? How do you know?

    Down: y gets smaller

  1. Here is the table for y = x2 + 4. Plot each point. Join them with a smooth curve.

    a smooth curve through (0, 4), (1, 5), (2, 8)
    x012y458

  2. Complete the table for y = x2 + 7.

    1, 4, 9 and 8, 11, 16
    x123x2 y

  3. Draw the graph of y = x2 on the grid in question 1.

    a smooth curve through (0, 0) and (3, 9)
Exit tickets to print