Consider the graph of the parabola:
Write down the coordinates of the \\ x-intercept.
State the equation of the vertical axis of symmetry.
State the coordinates of the vertex.
Determine whether the following statements are correct about this vertex.
The vertex is the maximum value of the graph.
The vertex lies on the axis of symmetry.
The vertex occurs at the x-intercept.
The vertex is the minimum value of the graph.
Consider the graph of the parabola:
Write down the coordinates of the \\ x-intercept.
State the coordinates of the vertex.
Determine whether the following statements are correct about this vertex.
The vertex is the minimum value of the graph.
The vertex lies on the axis of symmetry.
The vertex occurs at the x-intercept.
The vertex is the maximum value of the graph.
Consider the graph of the parabola:
How many x-intercepts does this parabola have?
State the coordinates of the vertex.
Is the vertex the maximum or minimum of this parabola?
Find the coordinates of the vertex of y = 2 x^{2} + 2 x - 4.
Consider the equation y = x^{2} + 10 x.
Write the equation in the form y = a \left(x - h\right)^{2} + k.
Find the coordinates of the vertex, in the form \left(a, b\right).
Write down the equation of the parabola that has the same shape as f \left( x \right) = 4 x^{2}, and vertex at \left( - 7 , - 3 \right).
For each of the following:
Rewrite the equation in the form y = \left(x + a\right)^{2} + b.
Hence determine the coordinates of the vertex.
Sketch the graph of the parabola.
y = x^{2} - 4 x + 2
y = x^{2} + 10 x
y = x^{2} + 4 x - 4
y = x^{2} + 5 x + 3
A parabola has the equation y = x^{2} - 4 x + 3.
Express the equation of the parabola in the form y = \left(x - h\right)^{2} + k by completing the square.
Find the y-intercept of the curve.
Find the coordinates of the vertex of the parabola.
Is the parabola concave up or down?
Hence, sketch the graph of y = x^{2} - 4 x + 3
A parabola has the equation y = x^{2} - 8 x + 7.
Find the x-intercepts of the equation.
Express the equation in the form y = a \left(x - h\right)^{2} + k by completing the square.
Find the coordinates of the vertex of the parabola.
Use the x-intercepts and the vertex to sketch the graph.
A parabola has the equation y = x^{2} + 6 x + 1.
Find the equation of the axis of symmetry.
Hence find the minimum value of y.
Sketch the graph of the parabola.
For each of the following:
Find the x-coordinate of the vertex.
Find the y-coordinate of the vertex.
Sketch the graph of the parabola.
y = x^{2} + 8 x + 8
y = - x^{2} + 6 x - 2
y = 2 x^{2} - 8 x - 2
y = - 2 x^{2} + 8 x - 7
y = - x^{2} - 5 x - 4
y = - 2 x^{2} - 10 x - 9
Consider the function y = x^{2} - 8 x + 15. Note that this function is not graphed below.
Find the equation of the axis of symmetry.
Hence find the minimum value of y.
Hence state the coordinates of the vertex of the curve.
Consider the graph of another quadratic function shown on the right. State the coordinates of its vertex.
What is the relationship between the graph of y = x^{2} - 8 x + 15 and the graph provided?
Consider the parabola defined by equation y = 2 \left(x - 3\right)^{2} + 2.
Write down the coordinates of the vertex.
Find the equation of the vertical axis of symmetry.
Write down the coordinates of the y-intercept.
Hence, sketch the graph of the parabola.
For each of the following:
Find the x-value of the vertex using the vertex formula.
Write down the coordinates of the vertex.
Find the y-intercept.
Hence, sketch the graph of the parabola.
y = x^{2} - 4 x + 11
y = - x^{2} - 4 x - 9
y = x^{2} - 2 x + 12
For each of the following:
Write the equation in the form y = \left(x - h\right)^{2} + k.
State the coordinates of the vertex.
State whether the vertex is the maximum or minimum of the parabola.
State the number of x-intercepts of the parabola.
y = x^{2} - 8 x + 18
y = - 4 x^{2} + 6 x - \dfrac{35}{12}
A parabola of the form y = \left(x - h\right)^{2} + k is symmetrical about the line x = - 3, and its vertex lies 5 units below the x-axis.
Find the equation of the parabola.
Sketch the graph of the parabola.
Consider the parabola defined by equation y = 4 \left(x - \dfrac{1}{3}\right)^{2} - \dfrac{3}{4}.
Write down the coordinates of the vertex.
State the equation of the vertical axis of symmetry for this parabola.
Write down the exact coordinates of the y-intercept.
Consider the equation y = 4 x^{2} + 24 x + 42.
Write the equation in the form y = \left(x - h\right)^{2} + k.
Find the coordinates of the vertex.
Find the coordinates of the new vertex when the parabola is reflected about the x-axis.
Consider the parabola y = - 4 - 10 \left(x - 1\right)^{2}.
Find the coordinates of the vertex.
The parabola is reflected about the y-axis. Find:
The new equation
The new vertex
Over the summer, Paul and his friends build a bike ramp to launch themselves into the local lake. Paul decides that the shape of the ramp will be parabolic, and reckons that the raddest parabola is given by the equation y = \dfrac{1}{4} \left(x + 4\right)^{2} + 5, where 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 10\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 9\text{ m}?
Sketch the graph of the ramp on a number plane.