Quadratic graphs: roots and turning points

The Maths Habit Handout to print

Work out y

  1. y = x2 + 2x − 3 when x = −3

    y = 0

  2. y = 6 − x2 when x = −2

    y = 2

  3. y = x2 − 4x + 1 when x = 2

    y = −3

A ball is kicked from the ground and lands 40 m away. How far along is it when it is at its highest?

Halfway: 20 m along

Roots
Where the graph crosses the x-axis.
Turning point
Where the curve turns: its lowest or highest point.
y-intercept
Where the graph crosses the y-axis.

Write down the roots.

Write down the
turning point.

y = x2 + 6x + 5

Roots

x = −5 and x = −1

y-intercept

(0, 5)

Turning point

(−3, −4)

y = x2 + 6x + 8

Roots

x = −4 and x = −2

y-intercept

(0, 8)

Turning point

(−3, −1)

y = x2 + 6x + 5

Roots

x = −5 and x = −1

y-intercept

(0, 5)

Turning point

(−3, −4)

y = −x2 − 2x + 3

Roots

x = −3 and x = 1

y-intercept

(0, 3)

Turning point

(−1, 4)

Quadratic graphs: roots and turning points worksheet, page 1

Quadratic graphs: roots and turning points worksheet, page 2

Answer sheet

  1. A quadratic graph has roots at x = 2 and x = 8. What is the x-coordinate of its turning point?

    5

  2. A quadratic graph has its turning point at (4, −9) and one root at x = 1. Find the other root.

    x = 7

  1. Write down the roots.

    x = 1 and x = 3
    xy−1012345−2−101234

  2. Write down the turning point. Is it a minimum or a maximum?

    (1, 4), maximum
    xy−2−101234−2−1012345

  3. The roots are x = −2 and x = 6. Find the x coordinate of the turning point.

    x = 2
Exit tickets to print