Textbook

10 Principles of Mathematics Nelson
Chapter

Chapter 3
Section

Geometric Properties Chapter Review

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Solutions
35 Videos

State whether each relation is quadratic.

a) `y = 4x - 5`

b) when

`x = -3, -2, -1, 0, 1, 2, 3`

,`y = 56,35, 18, 5, -4, -9, -10`

respectively

c) `y = 2x (x - 5)`

d)

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0.27mins

Q1

Discuss how the graph of the quadratic relation `y = 4x^2 + bx + 6`

changes as `a, b`

, and `c`

are changed.

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2.07mins

Q2

Find

- i. the equation of the axis of symmetry
- ii. the coordinates of the vertex
- iii. the y-intercept
- iv. the zeros

for

```
\displaystyle
y = x^2 -8x
```

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1.06mins

Q3a

Find

- i. the equation of the axis of symmetry
- ii. the coordinates of the vertex
- iii. the y-intercept
- iv. the zeros

for

```
\displaystyle
y = x^2 + 2x - 15
```

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1.17mins

Q3b

The x-intercepts of a quadratic relation are `-2`

and `5`

, and the second differences are negative.

a. Is the y-value of the vertex a maximum value or a minimum value? Explain.

b. Is the y-value of the vertex positive or negative? Explain.

c. Calculate the x-coordinate of the vertex.

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2.56mins

Q5

Use graphing technology to graph the parabola for each relation below. Then determine

- i) the x—intercepts
- ii) the equation of the axis of symmetry
- iii) the coordinates of the vertex

```
\displaystyle
y = -x^2 + 18x
```

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0.32mins

Q7a

Use graphing technology to graph the parabola for each relation below. Then determine

- i) the x—intercepts
- ii) the equation of the axis of symmetry
- iii) the coordinates of the vertex

```
\displaystyle
y = 6x^2 + 15x
```

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Q7b

What does `a`

in the equation `y = ax^2 + bx + c`

tell you about the parabola?

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0.47mins

Q8

The Rudy Snow Company makes custom snowboards. The company’s profit can be modelled with the relation ```
\displaystyle
y = -6x^2 + 42x - 60
```

, where x is the number of snowboards sold (in thousands) and `y`

is the profit (in hundreds of thousands of dollars).

a. How many snowboards does the company need to sell to break even?

b. How many snowboards does the company need to sell to maximize their profit?

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2.41mins

Q9

The x-intercepts of a parabola are `-2`

and `7`

, and the y-intercept is `-28`

.

a) Determine an equation for the parabola.

b) Determine the coordinates of the vertex.

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1.26mins

Q10

The x-intercepts are `-3`

and `7`

, and the y-coordinate of the vertex is `4`

.

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1.01mins

Q11b

The `x-`

intercepts are `-6`

and `2`

, and the `y-`

intercept is `-9`

.

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0.37mins

Q11c

The vertex is `(4, 0)`

, and the y-intercept is `8`

.

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0.44mins

Q11d

The x-intercepts are `-3`

and `3`

, and the parabola passes through the point `(2, 20)`

.

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0.40mins

Q11e

A bus company usually transports 12 000 people per day at a ticket price of `\$1`

. The company wants to raise the ticket price. For every `\$0.10`

increase in the ticket price, ,the number of riders per day is expected to decrease by 400. Calculate the ticket price that will maximize revenue.

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3.07mins

Q12

Identify the binomial factors and their products.

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0.29mins

Q13a

Identify the binomial factors and their products.

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0.18mins

Q13b

Expand and simplify.

`(x +5)(x + 4)`

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0.21mins

Q14a

Expand and simplify.

`(x - 2)(x - 5)`

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0.19mins

Q14b

Expand and simplify.

`(2x - 3)(2x + 3)`

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0.25mins

Q14c

Expand and simplify.

`(4x + 5)(3x - 2)`

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0.24mins

Q14d

Expand and simplify.

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

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0.32mins

Q14e

Expand and simplify.

`(6x -2)(5x + 7)`

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0.28mins

Q14f

Expand and simplify.

```
\displaystyle
(2x + 6)^2
```

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0.30mins

Q15a

Expand and simplify.

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

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0.43mins

Q15b

Expand and simplify.

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

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0.30mins

Q15c

Determine the equation of the parabola. Express your answer in standard form.

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0.44mins

Q16

Evaluate.

```
\displaystyle
2^{-3}
```

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0.14mins

Q19a

Evaluate.

```
\displaystyle
-5^{-1}
```

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0.11mins

Q19b

Evaluate.

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

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0.32mins

Q19c

Evaluate.

```
\displaystyle
(-9)^0
```

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0.18mins

Q19d

Evaluate.

```
\displaystyle
4^{-3}
```

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0.19mins

Q19e

Evaluate

```
\displaystyle
-(\frac{1}{6})^{-2}
```

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0.18mins

Q19f

Which is greater: `(\frac{1}{4})^2`

or `3^{-2}`

. Show your reason without using a calculator.

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0.18mins

Q20

For what positive values of `x`

is `x^2`

greater than `2^x`

?

How do you know?

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Q21