Recognising linear and quadratic graphs

The Maths Habit

You throw a ball to a friend. Sketch the path it takes through the air. Is it a straight line?

No: a curve, up and then back down

Linear
A straight line graph. Its equation has x but no x2.
Quadratic
A curved graph. Its equation has x2.

y = x + 1

y = x2 − 1

Linear or quadratic?

y = 3x − 5 Linear

Linear or quadratic?

y = x2 + 1 Quadratic

Where does it cross the y-axis?

y = x2 − 6 (0, −6)

Which equation matches the graph?

y = x + 3y = −x + 3y = −x2 + 3

Which equation matches the graph?

y = x2 + 2y = −x2 + 2y = −2x + 2

Which equation matches the graph?

Shapestraight linecurve
Typelinearquadratic
y = x − 4y = x2 − 4y = −x2 − 4

Which equation matches the graph?

Shapestraight linecurve
Typelinearquadratic
y = x2 − 1y = −x2 − 1y = x − 1

Which equation matches the graph?

Shapestraight linecurve
Typelinearquadratic
y = x − 4y = x2 − 4y = −x2 − 4

Which equation matches the graph?

Shapestraight linecurve
Typelinearquadratic
y = x2 + 3y = −x + 3y = −x2 + 3

Which equation matches the graph?

Shapestraight linecurve
Typelinearquadratic
y = x − 4y = x2 − 4y = −x2 − 4

Which equation matches the graph?

Shapestraight linecurve
Typelinearquadratic
y = 2x + 1y = x2 + 1y = −2x + 1

Which equation matches the graph?

Shapestraight linecurve
Typelinearquadratic
y = x − 4y = x2 − 4y = −x2 − 4

Which equation matches the graph?

Shapestraight linecurve
Typelinearquadratic
y = x2 + 4y = −x2 + 4y = −x + 4

Which equation matches the graph?

Shapestraight linecurve
Typelinearquadratic
y = x − 4y = x2 − 4y = −x2 − 4

Which equation matches the graph?

Shapestraight linecurve
Typelinearquadratic
y = x2 + 2y = −x2 − 2y = x2 − 2

Recognising linear and quadratic graphs worksheet, page 1

Recognising linear and quadratic graphs worksheet, page 2

Answer sheet

  1. Sketch y = x2 − 1 and y = 3 on the same axes. How many times do they cross?

    Twice

  2. A quadratic graph is the right way up and crosses the y-axis at (0, 5). Write a possible equation.

    y = x2 + 5

  1. Is y = 4 − x2 linear or quadratic?
    Where does it cross the y axis?

    Quadratic, (0, 4)

  2. Which of y = x2 + 2, y = 2 − x and y = 2 − x2 matches the graph?

    y = 2 − x2
    xy−3−2−10123−3−2−10123

  3. A quadratic graph is upside down and crosses the y axis at (0, −3). Write a possible equation for it.

    y = −x2 − 3
Exit tickets to print