Consider the parabola described by the function y = - 2 x^{2} + 2.
Is the parabola concave up or down?
Is the parabola more or less steep than the parabola y = x^{2}?
What are the coordinates of the vertex of the parabola?
Sketch the graph of y = - 2 x^{2} + 2.
A graph of f(x)=x^2 is shown on the right. Sketch the graph after it has undergone transformations resulting in the following functions:
g(x) = 4 x^{2} - 2
h(x) = 2 \left(x + 4\right)^{2}
Consider the two graphs. One of them has equation f(x) = x^{2} + 5.
What is the equation of the other graph?
Consider the quadratic function h \left( x \right) = x^{2} + 2.
Sketch the graph of the parabola h \left( x \right).
Plot the axis of symmetry of the parabola on the same graph.
What is the vertex of the parabola?
Consider the parabola described by the function y = \dfrac{1}{2} \left(x - 3\right)^{2}.
Is the parabola concave up or down?
Is the parabola more or less steep than the parabola y = x^{2} ?
What are the coordinates of the vertex of the parabola?
Sketch the graph of y = \dfrac{1}{2} \left(x - 3\right)^{2}.
Consider the equation y = \left(x - 3\right)^{2} - 1.
Find the x-intercepts.
Find the y-intercept.
Determine the coordinates of the vertex.
Sketch the graph.
Consider the quadratic function f \left( x \right) = - 3 \left(x + 2\right)^{2} - 4.
What are the coordinates of the vertex of this parabola?
What is the equation of the axis of symmetry of this parabola?
What is the y-coordinate of the graph of f \left( x \right) at x = -1?
Sketch the graph of the parabola.
Plot the axis of symmetry of the parabola on the same graph.
On a number plane, sketch the shape of a parabola of the form y = a \left(x - h\right)^{2} + k that has the following signs for a, h and k:
Consider the parabola y = \left(2 - x\right) \left(x + 4\right).
State the y-intercept.
State the x-intercepts.
Complete the table of values:
Determine the coordinates of the vertex of the parabola.
Sketch the graph of the parabola.
| x | -5 | -3 | -1 | 1 | 3 |
|---|---|---|---|---|---|
| y |
Consider the parabola y = \left(x - 3\right) \left(x - 1\right).
Find the y-intercept.
Find the x-intercepts.
State the equation of the axis of symmetry.
Find the coordinates of the turning point.
Sketch the graph of the parabola.
Consider the parabola y = x \left(x + 6\right).
Find the y-intercept.
Find the x-intercepts.
State the equation of the axis of symmetry.
Find the coordinates of the turning point.
Sketch the graph of the parabola.
Sketch the graph of the following:
Consider the function y = \left(x + 5\right) \left(x + 1\right).
Sketch the graph.
Sketch the graph of y = - \left(x + 5\right) \left(x + 1\right) on the same set of axes.
Consider the equation y = x^{2} - 6 x + 8.
Factorise the expression x^{2} - 6 x + 8.
Hence, or otherwise, find the x-intercepts of the quadratic function y = x^{2} - 6 x + 8
Find the coordinates of the turning point.
Sketch the graph of the function.
Consider the parabola y = x^{2} + x - 12.
Find the x-intercepts of the curve.
Find the y-intercept of the curve.
What is the equation of the vertical axis of symmetry for the parabola?
Find the coordinates of the vertex of the parabola.
Sketch the graph of y = x^{2} + x - 12.
A parabola has the equation y = x^{2} + 4 x-1.
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 parabola.
Find the vertex of the parabola.
Is the parabola concave up or down?
Hence, sketch the graph of y = x^{2} + 4 x-1.
Consider the quadratic y = x^{2} - 12 x + 32.
Find the zeros of the quadratic function.
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.
Hence, sketch the graph.
Consider the curve y = x^{2} + 6 x + 4.
Determine the axis of symmetry.
Hence, determine the minimum value of y.
Sketch the graph of the function.
Consider the function P \left( x \right) = - 2 x^{2} - 8 x + 2.
Find the coordinates of the vertex.
Sketch the graph.
Consider the equation y = 6 x - x^{2}.
Find the x-intercepts of the quadratic function.
Find the coordinates of the turning point.
Sketch the graph.
A parabola is described by the function y = 2 x^{2} + 9 x + 9.
Find the x-intercepts of the parabola.
Find the y-intercept for this curve.
Find the axis of symmetry.
Find the y-coordinate of the vertex of the parabola.
Sketch the graph.
Use your calculator or other handheld technology to graph the equations below. Then answer the following questions:
What is the vertex of the graph?
y = 4 x^{2} - 64 x + 263
y = - 4 x^{2} - 48 x - 140
Use your calculator or other handheld technology to graph y = - 3 x^{2} - 12.
What is the vertex of the graph?
Are there any x-intercepts?
For what values of x is the parabola decreasing?
Using a graphing calculator, sketch the curve y = x^{2} + 6.2 x - 7.
Determine the axis of symmetry.
Determine the minimum value of y.
Use a graphing calculator to sketch the parabola y = - 2 x^{2} + 16 x - 24.
Find the x-intercepts of the parabola.
Find the y-intercept of the parabola.
Find the axis of symmetry of the parabola.
Find the y-coordinate of the vertex of the parabola.
Consider the function y = - 0.72 x^{2} + \sqrt{5} x + 1.21.
Find the x-coordinate of the vertex to two decimal places.
Find the y-coordinate of the vertex to two decimal places.
Is the graph shown a possible viewing window on your calculator that shows the vertex and the x-intercepts?
Use a graphing calculator to find the \\x-intercepts to two decimal places.
Consider the function y = 0.91 x^{2} - 5 x - \sqrt{5}.
Find the x-coordinate of the vertex to two decimal places.
Find the y-coordinate of the vertex to two decimal places.
Is the graph shown a possible viewing window on your calculator that shows the vertex and the x-intercepts?
Use a graphing calculator to find the \\x-intercepts to two decimal places.
Consider the function f \left( x \right) = 2 x^{2} - 7 x + 2.
Starting with the interval \left[3, 4 \right], complete three applications of the binomial method:
| \text{Step} | a | b | f\left(a\right) | f\left(b\right) | c=\dfrac{a+b}{2} | f\left(c\right) |
|---|---|---|---|---|---|---|
| 1 | 3 | 4 | 2 | |||
| 2 | ||||||
| 3 | -1 | 0.375 |
Estimate the root of f \left( x \right) using the bisection method in the interval \\ \left[ 3, 4 \right]. Round your answer to three decimal places.
Consider the function f \left( x \right) = 2 x^{3} - 3 x - 1.
Starting with the interval \left[1, 2 \right], complete five applications of the binomial method:
| \text{Step} | a | b | f\left(a\right) | f\left(b\right) | c=\dfrac{a+b}{2} | f\left(c\right) |
|---|---|---|---|---|---|---|
| 1 | 1 | 2 | -2 | 9 | \dfrac{3}{2} | \dfrac{297}{4} |
| 2 | 1 | \dfrac{3}{2} | -2 | \dfrac{5}{4} | \dfrac{5}{4} | -\dfrac{27}{32} |
| 3 | \dfrac{5}{4} | \dfrac{3}{2} | -\dfrac{27}{32} | \dfrac{5}{4} | ||
| 4 | ||||||
| 5 | -\dfrac{2925}{16\,384} |
Estimate the root of f \left( x \right) using the bisection method in the interval \\ \left[ 1, 2 \right]. Round your answer to three decimal places.