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Solutions
25 Videos

Which scatter plot(s) could be modelled using a curve instead of a line of best fit? Explain.

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Q1

The table shows the operating revenue from dry cleaning and laundry services in Canada for the years from 2000 to 2004 in millions of dollars.

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

b) Describe the relationship between the year and the operating revenue.

c) Use your curve of best fit to predict the operating revenue in 2005.

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Q2

Use finite differences to determine whether each relation is linear, quadratic, or neither.

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Q3a

Use finite differences to determine whether each relation is linear, quadratic, or neither.

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Q3b

Use finite differences to determine whether each relation is linear, quadratic, or neither.

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Q3c

The flight of an aircraft from Toronto to Halifax can be modelled by the relation ` h = -3.5 t ^{2} + 210t`

, where *t* is the time, in minutes, and *h* is the height in metres.

a) Graph the relation.

b) How long does it take to fly from Toronto to Halifax?

c) What is the maximum height of the aircraft? At what time does the aircraft reach this height?

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Q4

Sketch the graph of each parabola. Describe the transformation from the graph of ` y = x^2`

.

` y = 3x^2`

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Q5a

Sketch the graph of each parabola. Describe the transformation from the graph of ` y = x^2`

.

` y =\dfrac{2}{3}x^2`

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Q5b

Sketch the graph of each parabola. Describe the transformation from the graph of ` y = x^2`

.

` y = x^2 -5`

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Q5c

Sketch the graph of each parabola. Describe the transformation from the graph of ` y = x^2`

.

` y = -\dfrac{1}{5}x^2`

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Q5d

Sketch the graph of each parabola. Describe the transformation from the graph of ` y = x^2`

.

` y = (x+7)^2`

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Q5e

Sketch the graph of each parabola. Describe the transformation from the graph of ` y = x^2`

.

` y = -x^2 + 5`

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Q5f

Copy and complete the table for each parabola. Replace the heading for the second column with the equation for the parabola.

` y = 2(x+2)^2`

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Q6a

Copy and complete the table for each parabola. Replace the heading for the second column with the equation for the parabola.

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

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Q6b

Copy and complete the table for each parabola. Replace the heading for the second column with the equation for the parabola.

` y = 3x^2 - 4`

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Q6c

` y = -5x^2 +3`

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Q6d

` y = 4(x+5)^2 +2`

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Q6e

` y = -\dfrac{1}{2} (x-4)^2 - 5`

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Q6f

a) Find an equation for the parabola with vertex (3,-1) that passes through the point (1,7).

b) Find an equation for the parabola with vertex (-5,-5) that passes through the point (3,27).

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Q7

Sketch a graph of each quadratic. Label the *x*-intercept and the vertex.

` y = 2(x+2)(x-4)`

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Q8a

Sketch a graph of each quadratic. Label the *x*-intercept and the vertex.

` y = -\dfrac{1}{2}(x-3)(x+1)`

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Q8b

The path of a soccer ball can be modelled by the equation ` h = -0.06d(d-50)`

, where *h* represents the height, in metres, of the soccer ball above the ground and *d* represents the horizontal distance, in metres, of the soccer ball from the player.

a) Sketch a graph of this relation.

b) At what horizontal distance does the soccer ball land?

c) At what horizontal distance does the soccer ball reach its maximum height? What is the maximum height?

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Q9

Evaluate.

` 4^{-2}`

` 3^{-5}`

` 5 ^{0}`

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Q10abc

Evaluate.

` (-3)^{-1}`

` (\dfrac{3}{4})^{-3}`

`(-7)^{0}`

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Q10def

Andy has $10 000 to invest. He decides to invest `\dfrac{1}{2}`

, or `2^{-1}`

, of his money in May, then invest half of the remaining amount in June, half again in July, and so on.

a) What fraction of his money remains after five months? After ten months?

b) What amount is remaining at the end of four months?

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Q11