Chapter

Chapter 4
Section

Chapter Test Quadratic Relations

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Solutions
17 Videos

Sketch a graph of each parabola. Label the coordinates of the vertex and the equation of the axis of symmetry.

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

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Q1a

Sketch a graph of each parabola. Label the coordinates of the vertex and the equation of the axis of symmetry.

```
\displaystyle
y = 2(x-5)^2
```

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Q1b

Sketch a graph of each parabola. Label the coordinates of the vertex and the equation of the axis of symmetry.

```
\displaystyle
y = -\frac{1}{3}(x+3)^2 + 4
```

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Q1c

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

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

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Q2a

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

```
\displaystyle
y = -4(x-1)(x - 9)
```

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Q2b

Determine an equation to represent each parabola.

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Q3a

Determine an equation to represent each parabola.

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Q3b

Evaluate

a) `4^0`

b) `5^{-1}`

c) `(-3)^{-3}`

d) `\left(\dfrac{3}{4}\right)^{-2}`

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Q4

The table shows the length of a spring under a specific load.

**a)** Use finite differences to determine whether this is a quadratic relation.

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

**c)** Use your curve of best fit to predict the length of the spring under a load of `8`

kg

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Q5

Board-feet are used to measure the total length, in feet, of boards that are `1`

inch thick and `1`

foot wide that can be cut from a tree to make lumber. You can use the equation `l=0.011a^2-0.68a+13.31`

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1.36mins

Q6

The St. Louis Gateway Arch in St. Louis, Missouri. was built in 1005 and was designed as a catenary. which is a curve that approximates a parabola. The arch is 102 m wide and 102 m tall.

a) Sketch a graph of the arch that is symmetrical about the y-axis.

b) Label the x-intercepts and the vertex.

c) Determine an equation to model the arch.

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2.21mins

Q7

When a car is travelling at a given speed, there is a minimum turn radius it can safely make. A particular car’s minimum radius can be calculated by `r = 0.6s^2`

, where `s`

is the speed, in kilometres per hour, and r is the turning radius, in metres. If the car uses tires with better grip, how does this affect the equation? Justify your response.

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1.26mins

Q8

The maximum viewing distance on a clear day is related to how high you are above the surface of Earth. This relationship can
be approximated by the formula ```
\displaystyle
h = \frac{3}{40}d^2
```

, where `d`

is the maximum distance, in
kilometres, and `h`

is your height, in metres, above the ground.

a) How high do you need to be in order to see a distance of 25 km?

b) How would the formula change if you were standing on a 20 m cliff?

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1.44mins

Q9

A volleyball’s height, `h`

, in metres, above the ground after 1 seconds is modelled by the relation `h = -4.9t^2 + 5t + 2`

.

a) Graph the relation.

b) What is the h-intercept? What does it represent?

c) How long will it take the volleyball to hit the ground? What feature on the graph models this? Explain your answer.

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2.46mins

Q10

An ant colony has 5000 ants on July 1 and doubles every year. This can be expressed as `N = 5000 \times 2^t`

, where `N`

represents the number of ants and `t`

represents time, in years.

a) Find the number of ants after 2, 3, 4, and 5 years.

b) What does `t = 0`

represent in this situation? What does `t = -2`

represent?

c) When were there 625 ants? Explain.

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Q11

The approximate cost of operating a certain car at a constant speed is given by the formula `C= 0.006(s-50)^2 + 20`

, for `10 \leq s \leq 130`

, where `s`

is the speed, in kilometres per hour, and `C`

is the most, in cents per kilometre. Use a graphing calculator to compare the operating costs, at different speeds, to those of a second vehicle with formula `C = 0.008(s-55)^2+15`

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Q12

a) Graph the following relations by developing a table of values and plotting points. Then, find the first and second differences.

```
\displaystyle
\begin{array}{lllll}
&y = x^2 -4x \\
&y = x^2 -4x + 5 \\
&y = x^2 -4x -2
\end{array}
```

b) Examine each graph and use its properties to write an equation in the form `y=(x-h)^2+k`

.

c) What conclusions can you make about the relation `y = x^2 - 4x + c`

for different values of `0`

?

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2.09mins

Q13