Textbook

11 Functions and Applications Nelson
Chapter

Chapter 4
Section

Chapter Review Quadratics Fun and App

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Solutions
31 Videos

Write in standard form.

```
\displaystyle
f(x) = (x + 3)^2 -7
```

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Q1a

Write in standard form.

```
\displaystyle
f(x) = -(x + 7)^2 +3
```

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Q1b

Write in standard form.

```
\displaystyle
f(x) = 2(x -1)^2 + 5
```

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Q1c

Write in standard form.

```
\displaystyle
f(x) = 2-3(x -2)^2 -4
```

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Q1d

Write the equation of the graph in vertex form.

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Q2a

Write the equation of the graph in vertex form.

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Q2b

Write the equation of the graph in vertex form.

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Q2c

Write the equation of the graph in vertex form.

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Q2d

Write in vertex form by completing the square.

```
\displaystyle
f(x) = x^2 + 2x - 15
```

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Q3a

Write in vertex form by completing the square.

```
\displaystyle
f(x) = -x^2 + 8x - 7
```

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Q3b

Write in vertex form by completing the square.

```
\displaystyle
f(x) = 2x^2 + 20x +16
```

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Q3c

Write in vertex form by completing the square.

```
\displaystyle
f(x) = 3x^2 + 12x +19
```

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Q3d

Write in vertex form by completing the square.

```
\displaystyle
f(x) = \frac{1}{2}x^2 -6x +26
```

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Q3e

Write in vertex form by completing the square.

```
\displaystyle
f(x) = 2x^2 + 2x +4
```

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Q3f

Determine the vertex, the axis of symmetry, the direction the parabola opens, and the number of zeros for each quadratic function. Sketch a graph of each.

```
\displaystyle
f(x) =3(x -5)^2 -2
```

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Q4a

Determine the vertex, the axis of symmetry, the direction the parabola opens, and the number of zeros for each quadratic function. Sketch a graph of each.

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

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Q4b

Determine the vertex, the axis of symmetry, the direction the parabola opens, and the number of zeros for each quadratic function. Sketch a graph of each.

```
\displaystyle
f(x) = 2x^2 + 4x + 7
```

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Q4c

```
\displaystyle
f(x) = -x^2 + 16x -64
```

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Q4d

Use the quadratic formula to determine the solutions.

```
\displaystyle
2x^2 -15x -8 = 0
```

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Q5a

Use the quadratic formula to determine the solutions.

```
\displaystyle
3x^2 +x + 7 = 0
```

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Q5b

Use the quadratic formula to determine the solutions.

```
\displaystyle
9x^2 = 6x -1
```

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Q5c

Use the quadratic formula to determine the solutions.

```
\displaystyle
2.6x^2 = -3.1x + 7
```

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Q5d

A T-ball player hits a ball from a tee that is 0.6 m tall. The height of the ball at a given time is modelled by the function `h(t) = -4.9t^2 + 7t + 0.6`

, where height, h(t), is in metres and time, `t`

, is in seconds.

a) What will the height be after 1s?

b) When will the ball hit the ground?

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Q6

Without solving, determine the number of real solutions of each equation.

```
\displaystyle
x^2 -6x + 9 = 0
```

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Q7a

Without solving, determine the number of real solutions of each equation.

```
\displaystyle
3x^2 -5x - 9 = 0
```

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Q7b

Without solving, determine the number of real solutions of each equation.

```
\displaystyle
16x^2 -8x + 1 = 0
```

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Q7c

For the function `f(x) = kx^2 + 8x + 5`

, what value(s) of `k`

will have

a) two distinct real solutions?

b) one real solution?

c) no real solution?

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Q8

The daily production cost, `C`

, of a special- edition toy car is given by the function `C(t) = 0.2t^2 - 10t + 650`

, where `C(t)`

is in dollars and `t`

is the number of cars made.

a) How many cars must be made to minimize the production cost?

b) Using the number of cars from part (a), determine the cost.

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Q9

The function `A(w) = 576w -2w^2`

models the area of a pasture enclosed by a rectangular fence, where `w`

is width in metres.

a) What is the maximum area that can be enclosed?

b) Determine the area that can be enclosed using a width of 20 m.

c) Determine the width of the rectangular pasture that has an area of `18 144 m^2`

.

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Q10

The vertical height of an arrow at a given time, `t`

, is shown in the table.

a) Determine an equation of a curve of good fit in vertex form.

b) State any restrictions on the domain and range of your function.

c) Use your equation from part (a) to determine when the arrow will hit a target that is 2 m above the ground.

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Q11

The table shows how many injuries resulted from motor vehicle accidents in Canada from 1984 to 1998.

a) Create a scatter plot, and draw a curve of good fit.

b) Determine an equation of a curve of good fit. Check the accuracy of your model using quadratic regression.

c) Check the accuracy of your model using quadratic regression.

d) Use one of your models to predict how many accidents will result in injury in 2002. Explain why you chose the model you did.

e) According to the quadratic regression model, when were accidents that resulted in injury at their maximum levels?

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Q12