Textbook

10 Principles of Mathematics Nelson
Chapter

Chapter 6
Section

Quadratic Equations Chapter Review

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Solutions
42 Videos

Solve the equation.

```
\displaystyle
(2x - 5)(3x +8) = 0
```

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Q1a

Solve the equation.

```
\displaystyle
x^2 + 12x + 32 = 0
```

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Q1b

Solve the equation.

```
\displaystyle
3x^2-10x - 8 = 0
```

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Q1c

Solve the equation.

```
\displaystyle
3x^2-5x + 5 = 2x^2 +4x -3
```

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Q1d

Solve the equation.

```
\displaystyle
2x^2 +5x -1= 0
```

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Q1e

Solve the equation.

```
\displaystyle
5x(x -1)+5 =7+x(1-2x)
```

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Q1f

The safe Stopping distance, in metres, for a boat that is travelling at 12 kilometres per hour in calm water can be modelled by the relation
```
\displaystyle
d = 0.002(2v^2+10v + 3000)
```

.

a) What is the safe stopping distance if the boat is travelling at 12 km/h?

b) What is the initial speed of the boat if it takes 15 m to stop?

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Q2

Determine the value of `c`

needed to create a perfect-square trinomial.

a) ```
\displaystyle
x^2 + 8x + c
```

b) ```
\displaystyle
x^2 - 16x + c
```

c) ```
\displaystyle
x^2 + 19x + c
```

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Q3abc

Determine the value of `c`

needed to create a perfect-square trinomial.

```
\displaystyle
2x^2 +12x + c
```

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Q3d

Determine the value of `c`

needed to create a perfect-square trinomial.

```
\displaystyle
-3x^2 + 15x + c
```

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Q3e

Determine the value of `c`

needed to create a perfect-square trinomial.

```
\displaystyle
0.1x^2 -7x + c
```

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Q3f

Complete the square to write each quadratic relation in vertex form.

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

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Q4a

Complete the square to write each quadratic relation in vertex form.

```
\displaystyle
y = x^2 -20x + 95
```

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Q4b

Complete the square to write each quadratic relation in vertex form.

```
\displaystyle
y = -3x^2 + 12x -2
```

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Q4c

Complete the square to write each quadratic relation in vertex form.

```
\displaystyle
y = 0.2x^2-0.4x + 1
```

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Q4d

Complete the square to write each quadratic relation in vertex form.

```
\displaystyle
y = 2x^2 +10x -12
```

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Q4e

Complete the square to write each quadratic relation in vertex form.

```
\displaystyle
y = -4.9x^2-19.6x + 12
```

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Q4f

Consider the relation ```
\displaystyle
y = -3x^2 -12x -2
```

a) Write the relation in vertex form by completing the square.

b) State the transformations that must be applied to `y =x^2`

to draw the graph of the relation.

c) Graph the relation.

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Q5

Cam has 46 m of fencing to enclose a meditation space on the grounds of his local hospital. He has decided that the meditation space should be rectangular, with fencing on only three sides. What dimensions will give the patients the maximum amount of meditation space?

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Q7

Solve the equation.

```
\displaystyle
3x^2-4x-10=0
```

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Q8a

Solve the equation.

```
\displaystyle
-4x^2+1 = -15
```

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Q8b

Solve the equation.

```
\displaystyle
x^2 =6x + 10
```

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Q8c

Solve the equation.

```
\displaystyle
(x-3)^2 -4 = 0
```

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Q8d

Solve the equation.

```
\displaystyle
(2x + 5)(3x -2) = (x + 1)
```

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Q8e

Solve the equation.

```
\displaystyle
1.5x^2-6.1x + 1.1 = 0
```

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Q8f

The height, `h`

, in metres, of a water balloon that is launched across a football stadium can be modelled by `h = -0.1x^2 + 2.4x + 8.1`

, where `x`

is the horizontal distance from the launching position, in metres. How far has the balloon travelled when it is `10`

m above the ground?

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Q9

A chain is hanging between two posts so that its height above the ground, `h`

, in centimetres, can be determined by `h = 0.0025x^2 - 0.9x + 120`

,
where `x`

is the horizontal distance from one post, in centimetres. How far from the post in the chain when it is 50 cm from the ground?

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Q10

Without solving, determine the number of solutions that the equation has.

```
\displaystyle
2x^2-5x+1=0
```

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Q11a

Without solving, determine the number of solutions that the equation has.

```
\displaystyle
-3.5x^2-2.1x - 1= 0
```

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Q11b

Without solving, determine the number of solutions that the equation has.

```
\displaystyle
x^2 + 5x + 8 = 0
```

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Q11c

Without solving, determine the number of solutions that the equation has.

```
\displaystyle
4x^2 -15= 0
```

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Q11d

Without solving, determine the number of solutions that the equation has.

```
\displaystyle
5(x^2 + 2x + 5) = -2(2x -25)
```

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0.50mins

Q11e

Without graphing, determine the number of x-intercepts that the relation has.

```
\displaystyle
y = (x-4)(2x + 9)
```

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Q12a

Without graphing, determine the number of x-intercepts that the relation has.

```
\displaystyle
y = -1.8(x- 3)^2 + 2
```

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Q12b

Without graphing, determine the number of x-intercepts that the relation has.

```
\displaystyle
y = 2x^2 + 8x + 14
```

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0.42mins

Q12c

Without graphing, determine the number of x-intercepts that the relation has.

```
\displaystyle
y = 2x(x - 5) + 7
```

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Q12d

Without graphing, determine the number of x-intercepts that the relation has.

```
\displaystyle
y = -1.4x^2 -4x - 5.4
```

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Q12e

Skydivers jump out of an airplane at an altitude of `3.5 km`

. The equation `H = 3500 - 5t^2`

models the altitude, `H`

, in metres, of the skydivers at `t`

seconds after jumping out of the airplane.

a) How far have the skydivers fallen after 10 s?

b) The skydivers open their parachutes at an altitude of 1000 m. How long did they free fall?

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Q13

The arch of the Tyne bridge in England is modelled by `h = -0.008x^2 * 1.296x + 107.5`

, where `h`

is the height of the arch above the riverbank and `x`

is the horizontal distance from the riverbank, both in metres. Determine the height of the arch.

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2.15mins

Q14

Tickets to a school dance cost $5, and the projected attendance is 300 people. For every $0.50 increase in the ticket price, the dance committee projects that attendance will decrease by 20. What ticket price will generate $1562.50 in revenue?

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Q15

A room has dimensions of 5 m by 8 m. A rug covers `\frac{3}{4}`

of the floor and leaves a uniform strip of the floor exposed. How wide is the strip?

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Q16

Two integers differ by 12 and the sum of their squares is 1040. Determine the integers.

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Q17