Textbook

10 Principles of Mathematics Nelson
Chapter

Chapter 3
Section

Geometric Properties Chapter Test

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Solutions
13 Videos

State the zeros, vertex, and equation of the axis of symmetry of the parabola at the right.

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Q1

The points `(-9, 0)`

and `(19, 0)`

lie on a parabola.

a) Determine an equation for its axis of symmetry.

b) The yâ€”coordinate of the vertex is -28. Determine an equation for the parabola in factored form.

c) Write your equation for part b) in standard form.

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Q2

Decide, without graphing, whether each data set can be modelled by a quadratic relation. Explain how you made your decision.

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Q3a

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Q3b

Sketch each graph. Label the intercepts and the vertex using their coordinates.

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

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Q4a

Sketch each graph. Label the intercepts and the vertex using their coordinates.

```
\displaystyle
y = -(x-6)(x + 4)
```

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Q4b

The population, `P`

, of a city is modelled by the equation `P = 14t^2 + 820t + 42 000`

, where tis the time in years.

When `t = 0`

, the year is 2008.

a) Determine the population in 2018.

b) When was population about 30 000?

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Q5

Expand and simplify.

```
\displaystyle
(3x -3)(5x + 2)
```

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Q6a

Expand and simplify.

```
\displaystyle
(3x -4y)(5x + 2y)
```

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Q6b

Expand and simplify.

```
\displaystyle
-5(x -4)^2
```

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Q6c

A toy rocket is placed on a tower and launched straight up. The table shows its height, `y`

, in metres above the ground after `x`

seconds.

a) What is the height of the tower?

b) How long is the rocket in flight?

c) Do the data in the table represent a quadratic relation? Explain.

d) Create a scatter plot. Then draw a curve of good fit.

e) Determine the equation of your curve of good fit.

f) What is the maximum height of the rocket?

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Q7

Evaluate.

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

b) ```
\displaystyle
-3^0
```

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Q9ab

Evaluate.

a) ```
\displaystyle
-(\frac{2}{3})^{-4}
```

b) ```
\displaystyle
-5^{-3}
```

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Q9cd