For the following equations:
Complete the table of values:
Plot the graph of the parabola.
| x | - 3 | - 2 | - 1 | 0 | 1 | 2 | 3 |
|---|---|---|---|---|---|---|---|
| y |
y = 3 x^{2} + 2
y = 3 x^{2} - 3
y = - 3 x^{2} + 4
y = - 2 x^{2} - 4
For the following equations:
Complete the given table of values.
Plot the graph of the parabola.
Find the maximum y -value.
Find the coordinates of the vertex.
y = - \left(x - 3\right)^{2}
| x | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| y |
y = - \left(x + 3\right)^{2}
| x | -5 | -4 | -3 | -2 | -1 |
|---|---|---|---|---|---|
| y |
What feature is at the point \left(h, k\right) on the parabola defined by the equation: y = a \left(x - h\right)^{2} + k
Consider the following parabola:
Find the coordinates of the vertex.
Given that the graph has equation of the form y = a \left(x - h\right)^{2} + k, find the equation of the parabola.
For the following sentences:
Write the equations in the form y=\left(x + a\right)^{2} + b.
Find the coordinates of the vertex.
Sketch the graph of the parabola.
For the following equations:
Describe its successive transformations from y = x^{2}.
Find the coordinates of the vertex.
Sketch the graph of the parabola.
Find the axis of symmetry.
y = \left(x - 3\right)^{2} - 4
y = - \left(x + 2\right)^{2} - 5
For the following equations:
Find the x-intercepts.
Find the y-intercept.
Find the coordinates of the vertex.
Sketch the graph of the parabola.
y = \left(x - 2\right)^{2} - 16
y = \left(x + 2\right)^{2} + 4
y = - \left(x + 4\right)^{2} + 9
y = 4 - \left(x - 1\right)^{2}
For the following equations:
Find the y-intercept.
Is the graph concave up or down?
Find the minimum y-value.
Find the coordinates of the vertex.
Sketch the graph of the parabola.
Find the axis of symmetry.
y = \left(x - 1\right)^{2} + 1
y = - \left(x + 3\right)^{2} + 3
Consider the parabola described by the equation:y = 2 \left(x - 1\right)^{2} - 3
Is the parabola concave up or down?
Is the parabola more or less steep than the parabola y = x^{2}?
Find the coordinates of the vertex of the parabola.
Sketch the graph of this function.
Consider the parabola described by the equation:y = - \dfrac{1}{3} \left(x - 2\right)^{2} + 2
Is the parabola concave up or down?
Is the parabola more or less steep than the parabola y = - x^{2}?
Find the coordinates of the vertex of the parabola.
Sketch the graph of this function.
Consider the parabola described by the equation:y = - 3 \left(x + 5\right)^{2} - 4
Find the coordinates of the vertex of this parabola.
Find the axis of symmetry of this parabola.
Find the y-coordinate of the graph at x = - 4.
Sketch the graph of this function.
Sketch the axis of symmetry of the parabola on the same number plane.
For the following transformations:
Find the equation of the resulting parabola.
Find the minimum y-value.
Find the x-value that results in the minimum y-value.
Find the axis of symmetry.
Sketch the graph of the resulting parabola.
The graph of y = \left(x + 6\right)^{2} is translated 6 units up.
The graph of y = \left(x - 3\right)^{2} is translated 3 units down.
The graph of y = - \left(x + 3\right)^{2} is translated 2 units up.
Find the equation of the resulting parabola.
Find the maximum x and y-values.
Find the axis of symmetry.
Find the coordinates of the vertex.
Sketch the graph of the resulting parabola.
Sketch the graph of y = \left(x - 4\right)^{2} and its transformation y = 2 \left(x - 4\right)^{2} - 4 on the same number plane.
Sketch the graph of the function f\left(x\right) = x^{2} and its transformation g\left(x\right) = - 3 \left(x + 2\right)^{2} + 5 on the same number plane.
A parabola has the equation: y = x^{2} + 4 x-1
Express the equation in the form y = \left(x - h\right)^{2} + k .
Find the y-intercept of the curve.
Find the coordinates of the vertex.
Is the parabola concave up or down?
Sketch the graph of the function.
Consider the quadratic function:y = x^{2} - 12 x + 32
Find the zeros of the quadratic function by completing the square.
Express the equation in the form y = a \left(x - h\right)^{2} + k by completing the square.
Find the coordinates of the vertex.
Sketch the graph of the function.
The following parabola is symmetrical about the line x = 2, and its vertex lies 6 units below the x-axis. It has the form:y = \left(x - h\right)^{2} + k
Find the equation of the parabola.
Sketch the graph of the prabola.
A parabola has x-intercepts at \left(1, 0\right) and \left( - 5 , 0\right) and is of the form:y = \left(x - h\right)^{2} + k
Find the axis of symmetry.
Find the equation of the parabola.
Over the summer, Susana and her friends build a bike ramp to launch themselves into the local lake. Susana decides that the shape of the ramp will be parabolic, and reckons that the parabola is given by the equation: y = \dfrac{1}{4} \left(x + 2\right)^{2} + 2where y is the height in metres above the ground, and x is the horizontal distance in metres from the edge of the lake.
If the ramp starts 6 \text{ m} back from the edge of the lake, how high is the start of the ramp?
At what height will the rider leave the ramp?
At what other distance x is the rider also at a height of 3 \text{ m}?
Graph the shape of the ramp on a number plane.
