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Cogito

Integrated Math 2 · Chapter 1 · Lesson 3

Practice Worksheet

Modelling with Quadratics

Projectiles, areas, and maximum values.

12 problems · about 21 minutes · F-IF.B.4, A-CED.A.1

NameDate

Figure — use these to answer the problems

Set a negative and b positive. That downward parabola is the height of a thrown object against time.
-8-8-6-6-4-4-2-222446688
y = -1x² + 6x + 0
a-1
b, launch speed6
c, starting height0
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. h = −5t² + 40t. At what time is the height greatest, in seconds?

    Answer

  2. What does the vertex give in a projectile model?

    • The greatest height and the time it occurs.
    • When the object lands.

  3. h = −5t² + 20t at t = 1. What is h, in metres?

    Answer

  4. h = −5t² + 20t at t = 2. What is h?

    Answer

  5. h = −5t² + 30t. At what time is the height greatest, in seconds?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. h = −5t² + 10t + 8. What is the starting height, in metres?

    Answer

  2. A rectangle has perimeter 40. What side length maximises the area?

    Answer

  3. That maximum area, in square units?

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Match each feature with its meaning in a height model.

    Draw a line from each item on the left to its match on the right.

    • The vertex
    • The positive root
    • The y-intercept
    • Greatest height and when it happens
    • When the object lands
    • The starting height

  2. A rectangle has perimeter 24. What side maximises the area?

    Answer

  3. The Peak

    h = −5t² + 20t. At what time, in seconds, is the height greatest?

    Answerseconds

  4. The Landing

    Same model. At what time does the ball return to the ground, other than t = 0?

    Answerseconds