Consider the equation x = y^{2}.
Find the x-value of the point which has a y-coordinate of 4.
Find the x-value of the point which has a y-coordinate of - 4.
Find the distance between these two points.
Determine whether the following is true of the graph of x = y^{2}:
There are always two points that contain the same x-coordinate, except for x = 0.
There are always two points that contain the same y-coordinate, except for y = 0.
Consider the equation x = y^{2}.
Make y the subject.
Explain why the graph of y = \pm \sqrt{x} has symmetry.
What is the equation of the axis of symmetry of x = y^{2} ?
Consider the graph of the relation x = - y^{2}.
State two functions that can be combined together to form the same graph as x = - y^{2}.
Over which values of x is the relation defined?
The point \left(k^{2} - 28 k - 35, 2 k-1\right) lies on the curve x = y^{2}. Find the values of k.
For each of the following parabolas:
State the coordinates of the vertex.
State whether the parabola opens upward or downwards.
y = - \left(x + 5\right)^{2} + 4
y - 5 = - \left(x + 4\right)^{2}
\left(x - 3\right)^{2} = y + 2
Consider the parabola with equation \left(x + 1\right)^{2} = 8 y.
State the coordinates of the vertex of the parabola.
Determine the distance of the point \left(3, 2\right) from the vertex.
For each of the following parabolas:
State the coordinates of the vertex.
State whether the parabola opens to the left or right.
Find the coordinates of the vertex of the parabola: x = \left(y + 3\right)^{2} - 4.
Consider the parabola with equation x = 2 \left(y - 4\right)^{2} - 1.
Is this a horizontal or vertical parabola?
Does the parabola open left or right?
What are the coordinates of the vertex?
For each of the following parabolas:
State the coordinates of the vertex.
In which direction does the parabola open?
y - 4 = \left(x + 5\right)^{2}
y - 2 = - \left(x + 5\right)^{2}
x - 4 = \left(y + 2\right)^{2}
x - 5 = - \left(y + 3\right)^{2}
Find the coordinates of the vertex of the parabola with equation x = - 3 y^{2} + 12 y + 11
Consider the parabola x = y^{2}.
State the range of values of x for which the relation is defined.
Complete the table for the values of x:
Plot the points from the table of values on a number plane.
Sketch the graph of the curve that passes through the plotted points.
| x | |||||||
|---|---|---|---|---|---|---|---|
| y | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
How many points on the graph correspond to any one particular value of x, for x > 0?
Consider the parabola x = - \dfrac{1}{4} y^{2}.
Complete the following table of coordinate pairs for the given equation:
Sketch the graph of the parabola.
| x | |||||||
|---|---|---|---|---|---|---|---|
| y | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
Consider the parabola x = y^{2} whose graph is shown:
How many points on the graph have an \\x-coordinate of 81?
State the values of y that correspond to an x-value of 81.
Consider the parabola x = y^{2} + 4.
Complete the following table of coordinate pairs:
Sketch the graph of the parabola.
| x | |||||
|---|---|---|---|---|---|
| y | -2 | -1 | 0 | 1 | 2 |
Consider the parabola x = \left(y - 4\right)^{2}.
Complete the following table of coordinate pairs:
Sketch the graph of the parabola.
| x | ||||||
|---|---|---|---|---|---|---|
| y | 2 | 3 | 4 | 5 | 6 | 7 |
Consider the parabola x = \dfrac{1}{4} y^{2}.
Sketch the graph of the parabola.
State the coordinates of the x-intercept.
Consider the parabola x = - y^{2} + 2.
Complete the following table of coordinate pairs:
Sketch the graph of the parabola.
State the coordinates of the x-intercept.
| x | |||||
|---|---|---|---|---|---|
| y | -2 | -1 | 0 | 1 | 2 |
For each of the following equations:
Sketch the graph of the parabola.
State the domain of the function in interval notation.
State the range of the function in interval notation.
y - 5 = x^{2}
y = \left(x + 4\right)^{2}
x + 2 = y^{2}
x = \left(y - 3\right)^{2}
y + 5 = \left(x + 2\right)^{2}
x - 1 = \left(y - 3\right)^{2}
y - 2 = - \dfrac{1}{3} \left(x - 1\right)^{2}
x - 2 = - 3 \left(y - 5\right)^{2}
y = x^{2} + 4 x + 3
x = y^{2} - 4 y + 3
y + 3 x^{2} - 24 x + 53 = 0
x + 3 y^{2} - 30 y + 78 = 0
Consider the graphs of y= x^{2} and
x = y^{2} shown:
Describe the transformation required to transform y= x^{2} into x = y^{2}.