3.05 Plotting parabolas
For the following equations:
Find the y-intercept.
Find the x-intercepts.
Complete the table of values for the equation.
Find the coordinates of the vertex.
Sketch the graph of the parabola.
y = x \left(x - 4\right)
| x | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| y |
y = \left(x - 2\right) \left(x - 6\right)
| x | 0 | 2 | 4 | 6 | 8 |
|---|---|---|---|---|---|
| y |
y = \left(1 - x\right) \left(x + 5\right)
| x | - 6 | - 4 | - 2 | 0 | 2 |
|---|---|---|---|---|---|
| y |
| x | -5 | -4 | -3 | -2 | -1 |
|---|---|---|---|---|---|
| y |
For the following equations:
Find the y-intercept.
Find the x-intercepts.
Find the axis of symmetry.
Find the coordinates of the vertex.
Sketch the graph of the parabola.
y = x \left(x + 4\right)
y = x \left(4 - x\right)
y = \left(x - 2\right) \left(x - 6\right)
y = \left(x - 3\right) \left(x + 1\right)
y = \left(5 - x\right) \left(x + 1\right)
y = \left(1 - x\right) \left(3 - x\right)
Consider the equation: y = \left(4 - x\right) \left(x - 20\right)
Find the x-intercepts.
Find the axis of symmetry.
Describe the concavity of the parabola.
Does the graph have a minimum or a maximum value?
Find the minimum or maximum y-value of the equation.
Consider the following graph:
Find the y-intercept.
Find the equation of the parabola in factorised form.
A parabola has x-intercepts at x = 1 and x = - 7.
Find the equation of the parabola.
Find the y-intercept.
Sketch the graph of the parabola.
A parabola has x-intercepts at x = \pm\sqrt{3}.
Find the equation of the parabola in expanded form.
Find the y-value of the point on the parabola where x = 1.
Sketch the graph of the parabola.
Consider the functions: f(x) = \left(x - 2\right) \left(x - 4\right) \,\,\text{ and } \,\, g(x) = 2 \left(x - 2\right) \left(x - 4\right)
Find the y-intercept of g(x).
Sketch the graph of f(x) and g(x) on the same number plane.
Graph each pair of equations on the same number plane:
\text{Equation 1: } y = x \left(x + 5\right) \\ \text{Equation 2: } y = x \left(x - 3\right)
\text{Equation 1: } y = \left(x + 2\right) \left(x - 1\right) \\ \text{Equation 2: } y = \left(x + 4\right) \left(x - 1\right)
For the following equations:
Factorise the expression.
Find the x-intercepts.
Find the y-intercept.
Complete the given table of values.
Find the coordinates of the vertex.
Sketch the graph of the parabola.
| x | - 3 | - 2 | -1 | 0 | 1 |
|---|---|---|---|---|---|
| y |
| x | - 8 | - 6 | - 4 | - 2 | 0 |
|---|---|---|---|---|---|
| y |
For the following equations:
Factorise the expression.
Find the x-intercepts.
Find the coordinates of the vertex.
Sketch the graph of the parabola.
y = 4 x - x^{2}
y = x^{2} + 6 x + 8
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.
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.
For the following equations:
Describe the concavity of the parabola.
Find the x-intercepts.
Find the y-intercept.
Find the axis of symmetry.
Find the coordinates of the vertex.
Sketch the graph of the parabola.
y = x^2 -4x+3
y = x^{2} - 36
y = - x^{2} + 4
y = x^{2} + 4 x + 3
y = x^{2} + 6 x + 5
y = x^{2} - 8 x + 15
y = - x^{2} + 2 x + 24
y = - x^{2} - 2 x + 8
y = x^{2} - 2 x - 8
y = 8 + 2 x - x^{2}
y = x^{2} + 2 x - 3
y = 2 x^{2} + 9 x + 9
The height h, in metres, reached by a ball thrown in the air after t seconds is given by the equation: h = 10 t - t^{2}
Complete the table of values for h = 10 t - t^{2}:
| t | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| h |
Graph the relationship h = 10 t - t^{2}.
Find the height of the ball after 5.5 seconds have passed.
Find the maximum height reached by the ball.
The height h, in metres, reached by a ball thrown in the air after t seconds is given by the equation: h = 14 t - t^{2}
Assuming the ball starts at height 0, find the time t when it will hit the ground.
Graph the relationship h = 14 t - t^{2}.
Find the height of the ball after 9.5 seconds have passed.
Find the maximum height reached by the ball.
When an object is thrown into the air, its height above the ground is given by the equation:
h = 163 + 38 s - s^{2}where s is its horizontal distance from where it was thrown.
Graph the relationship h = 163 + 38 s - s^{2}.
Find s, how far horizontally the object is from where it was thrown at the point when it reaches its greatest height above the ground.
Find the maximum height reached by the object.