Which scatter plot(s) could be modelled using a curve instead of a line of best fit? Explain.
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.
Use finite differences to determine whether each relation is linear, quadratic, or neither.
Use finite differences to determine whether each relation is linear, quadratic, or neither.
Use finite differences to determine whether each relation is linear, quadratic, or neither.
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?
Sketch the graph of the parabola. Describe the transformation from the graph of y = x^2.
\displaystyle
y = x^2 -6
Sketch the graph of the parabola. Describe the transformation from the graph of y = x^2.
\displaystyle
y = -0.5x^2
Sketch the graph of the parabola. Describe the transformation from the graph of y = x^2.
\displaystyle
y = (x - 2)^2
Sketch the graph of the parabola. Describe the transformation from the graph of y = x^2.
\displaystyle
y = -2x^2
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
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
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
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
Sketch a graph of each quadratic. Label the x-intercepts and the vertex.
\displaystyle
y = -(x + 5)(x -7)
Sketch a graph of each quadratic. Label the x-intercepts and the vertex.
\displaystyle
y = 2(x - 3)(x +1)
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?
Evaluate
\displaystyle
7^{-2}
Evaluate
\displaystyle
13^0
Evaluate
\displaystyle
10^{-5}
Evaluate
\displaystyle
(-34)^0
Evaluate
\displaystyle
(-6)^{-1}
Evaluate
\displaystyle
(-7)^{-2}
Evaluate
a)
\displaystyle
6^0
b)
\displaystyle
(-\frac{2}{5})^{-3}
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?