Chapter

Chapter 4
Section

Chapter Review Quadratic Relations

Purchase this Material for $8

You need to sign up or log in to purchase.

Subscribe for All Access
You need to sign up or log in to purchase.

Solutions
25 Videos

Which scatter plot(s) could be modelled using a curve instead of a line of best fit? Explain.

Buy to View

0.35mins

Q1

A scientist tested the strength of wood beams by securing beams of various lengths and placing a 500—kg mass at the end of each beam. The table shows the mean deflections, in centimetres.

a) Make a scatter plot of the data. Draw a curve of best fit.

b) Describe the relationship between the length of the beam and the deflection.

c) Use your curve of best fit to predict the deflection of a 6.0-m-long beam.

Buy to View

Q2

Use finite differences to determine whether each relation is linear, quadratic, or neither.

Buy to View

0.41mins

Q3a

Use finite differences to determine whether each relation is linear, quadratic, or neither.

Buy to View

0.36mins

Q3b

Use finite differences to determine whether each relation is linear, quadratic, or neither.

Buy to View

Q3c

The flight of an aircraft from Toronto to Montreal can be modelled by the relation `h = -2.5t^2 + 200t`

, where `t`

is the time, in minutes, and `h`

is the height, in metres.

a) How long does it take to fly from Toronto to Montreal?

b) What is the maximum height of the aircraft? At what time does the aircraft reach this height?

Buy to View

1.46mins

Q4

Sketch the graph of the parabola. Describe the transformation from the graph of `y = x^2`

.

```
\displaystyle
y = x^2 -6
```

Buy to View

0.21mins

Q5a

Sketch the graph of the parabola. Describe the transformation from the graph of `y = x^2`

.

```
\displaystyle
y = -0.5x^2
```

Buy to View

1.00mins

Q5b

Sketch the graph of the parabola. Describe the transformation from the graph of `y = x^2`

.

```
\displaystyle
y = (x - 2)^2
```

Buy to View

0.40mins

Q5c

Sketch the graph of the parabola. Describe the transformation from the graph of `y = x^2`

.

```
\displaystyle
y = -2x^2
```

Buy to View

0.39mins

Q5d

State the following for the given parabola.

- Vertex
- Axis of symmetry
- Stretch or compression factor relative to
`y=x^2`

- Direction of opening
- Values x may take
- Values y may take

```
\displaystyle
y =(x - 1)^2 -4
```

Buy to View

Q6a

State the following for the given parabola.

- Vertex
- Axis of symmetry
- Stretch or compression factor relative to
`y=x^2`

- Direction of opening
- Values x may take
- Values y may take

```
\displaystyle
y =2(x + 3)^2 + 1
```

Buy to View

Q6b

State the following for the given parabola.

- Vertex
- Axis of symmetry
- Stretch or compression factor relative to
`y=x^2`

- Direction of opening
- Values x may take
- Values y may take

```
\displaystyle
y =\frac{1}{4}(x - 5)^2 + 1
```

Buy to View

0.39mins

Q6c

State the following for the given parabola.

- Vertex
- Axis of symmetry
- Stretch or compression factor relative to
`y=x^2`

- Direction of opening
- Values x may take
- Values y may take

```
\displaystyle
y = -(x + 2)^2 + 6
```

Buy to View

Q6d

Sketch a graph of each quadratic. Label the x-intercepts and the vertex.

```
\displaystyle
y = -(x + 5)(x -7)
```

Buy to View

Q7a

Sketch a graph of each quadratic. Label the x-intercepts and the vertex.

```
\displaystyle
y = 2(x - 3)(x +1)
```

Buy to View

Q7b

The path of a football can be modelled by the equation `h = -0.0625d(d - 56)`

, where `h`

represents the height, in metres, of the football above the ground and `d`

represents the horizontal distance, in metres, of the football from the player.

a) At what horizontal distance does the football land?

b) At what horizontal distance does the football reach its maximum height? What is its maximum height?

Buy to View

1.30mins

Q8

Evaluate

```
\displaystyle
7^{-2}
```

Buy to View

0.09mins

Q9a

Evaluate

```
\displaystyle
13^0
```

Buy to View

0.19mins

Q9b

Evaluate

```
\displaystyle
10^{-5}
```

Buy to View

0.18mins

Q9c

Evaluate

```
\displaystyle
(-34)^0
```

Buy to View

0.07mins

Q9d

Evaluate

```
\displaystyle
(-6)^{-1}
```

Buy to View

0.13mins

Q9e

Evaluate

```
\displaystyle
(-7)^{-2}
```

Buy to View

0.15mins

Q9f

Evaluate

a) ```
\displaystyle
6^0
```

b) ```
\displaystyle
(-\frac{2}{5})^{-3}
```

Buy to View

0.42mins

Q9gh

Joan won a multi-million dollar lottery. She decides to give $1 000 000 of her winnings to charity. Her plan is to give `\frac{1}{2}`

or `2^{-1}`

, to charity in January, and then give half of the remaining amount in February, half again in March, and so on.

a) What fraction remains after 6 months?

b) What fraction remains after 12 months?

c) Write each fraction as a power of 2 with a negative exponent.

d) What amount is remaining at the end of the year?

Buy to View

Q10