State whether the graphs below represent a nonlinear relationship between x and y:
Consider the table of values below:
Is revenue changing at a constant rate?
Is the relationship between time and revenue linear or nonlinear?
| Time | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Revenue | 5 | 14 | 25 | 36 | 47 |
Consider the table of values for y = 2 x^{2}. Complete the missing values in the table.
| x | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
|---|---|---|---|---|---|---|---|
| y | 18 | 2 | 0 | 2 | 18 |
Consider the table of values for
y = 2 x^{2} - x. Complete the missing values in the table.
| x | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
|---|---|---|---|---|---|---|---|
| y | 21 | 3 | 0 | 1 | 6 |
Consider the function y = 2 x^{2}.
Complete the table of values.
Does y = 2 x^{2} represent a linear or nonlinear relationship?
| x | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| y |
For each of the following functions:
Complete a table of values of the form:
| x | -2 | -1 | 0 | 1 | 2 |
|---|---|---|---|---|---|
| y |
Sketch the graph on a number plane.
Consider the function y = x^{2}.
Complete the table of values:
| x | -2 | -1 | 0 | 1 | 2 |
|---|---|---|---|---|---|
| y |
Sketch the graph on a number plane.
Are the y values ever negative?
What is the minimum y value?
Write down the equation of the axis of symmetry.
Consider the equation y = - x^{2}.
Complete the table of values:
| x | -2 | -1 | 0 | 1 | 2 |
|---|---|---|---|---|---|
| y |
Sketch the graph on a number plane.
Are the y values ever positive?
What is the maximum y value?
Write down the equation of the axis of symmetry.
Vincent is training for a remote control plane aerobatics competition. He wants to fly the plane along the path of a parabola, and so has chosen the equation y = 3 x^{2}, where y is the height in meters of the plane from the ground, and x is the horizontal distance in meters of the plane from its starting point.
Complete the following table of values of the height and distance.
| x\text{ (m)} | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| y\text{ (m)} |
Plot the shape of the path of the plane.
State the lowest height of the plane.
State the x value that corresponds to this minimum y value.
State the coordinates of the vertex.