Chapter
Chapter 4
Section
Solutions 25 Videos

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

0.35mins
Q1

A scientist tested the strength of wood beams by securing beams of various lengths and placing a 500—kg mass at the end of each beam. The table shows the mean deflections, in centimetres.

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

b) Describe the relationship between the length of the beam and the deflection.

c) Use your curve of best fit to predict the deflection of a 6.0-m-long beam.

Q2

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

0.41mins
Q3a

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

0.36mins
Q3b

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

Q3c

The flight of an aircraft from Toronto to Montreal can be modelled by the relation h = -2.5t^2 + 200t, where t is the time, in minutes, and h is the height, in metres.

a) How long does it take to fly from Toronto to Montreal?

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

1.46mins
Q4

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

 \displaystyle y = x^2 -6 

0.21mins
Q5a

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

 \displaystyle y = -0.5x^2 

1.00mins
Q5b

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

 \displaystyle y = (x - 2)^2 

0.40mins
Q5c

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

 \displaystyle y = -2x^2 

0.39mins
Q5d

State the following for the given parabola.

• Vertex
• Axis of symmetry
• Stretch or compression factor relative to y=x^2
• Direction of opening
• Values x may take
• Values y may take

\displaystyle y =(x - 1)^2 -4 

Q6a

State the following for the given parabola.

• Vertex
• Axis of symmetry
• Stretch or compression factor relative to y=x^2
• Direction of opening
• Values x may take
• Values y may take

\displaystyle y =2(x + 3)^2 + 1 

Q6b

State the following for the given parabola.

• Vertex
• Axis of symmetry
• Stretch or compression factor relative to y=x^2
• Direction of opening
• Values x may take
• Values y may take

\displaystyle y =\frac{1}{4}(x - 5)^2 + 1 

0.39mins
Q6c

State the following for the given parabola.

• Vertex
• Axis of symmetry
• Stretch or compression factor relative to y=x^2
• Direction of opening
• Values x may take
• Values y may take

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

Q6d

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

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

Q7a

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

\displaystyle y = 2(x - 3)(x +1) 

Q7b

The path of a football can be modelled by the equation h = -0.0625d(d - 56), where h represents the height, in metres, of the football above the ground and d represents the horizontal distance, in metres, of the football from the player.

a) At what horizontal distance does the football land?

b) At what horizontal distance does the football reach its maximum height? What is its maximum height?

1.30mins
Q8

Evaluate

 \displaystyle 7^{-2} 

0.09mins
Q9a

Evaluate

 \displaystyle 13^0 

0.19mins
Q9b

Evaluate

 \displaystyle 10^{-5} 

0.18mins
Q9c

Evaluate

 \displaystyle (-34)^0 

0.07mins
Q9d

Evaluate

 \displaystyle (-6)^{-1} 

0.13mins
Q9e

Evaluate

 \displaystyle (-7)^{-2} 

0.15mins
Q9f

Evaluate

a)  \displaystyle 6^0 

b)  \displaystyle (-\frac{2}{5})^{-3} 

0.42mins
Q9gh

Joan won a multi-million dollar lottery. She decides to give \$1 000 000 of her winnings to charity. Her plan is to give \frac{1}{2} or 2^{-1}, to charity in January, and then give half of the remaining amount in February, half again in March, and so on.

a) What fraction remains after 6 months?

b) What fraction remains after 12 months?

c) Write each fraction as a power of 2 with a negative exponent.

d) What amount is remaining at the end of the year?