Topics
2. Non-linear relationships
topic badge
AustraliaNSW
Year 12

2.02 Graphing quadratic functions with technology

Lesson
Worksheet
Practice
Worksheet
Graph parabolas using technology
1

Using technology, graph each of the given functions and hence answer the following questions:

i

Does this parabola have a maximum or a minimum value?

ii

Find the minimum/maximum y-value on the graph.

iii

Describe where the axis of symmetry lies.

a
y = x^{2}
b
y = - x^{2}
2

Using technology, graph each of the given functions and hence answer the following questions:

i

Does this parabola have a maximum or a minimum value?

ii

Find the minimum/maximum y-value on the graph.

iii

Describe where the axis of symmetry lies.

iv

Use technology to graph y = x^{2} on the same axes. Describe the similarities and differences between this graph and that of the given function in terms of the axis of symmetry and minimum/maximum values.

a
y = 2 x^{2}
b
y = \dfrac{1}{3} x^{2}
c
y = x^{2} - 7
3

Using technology, graph y = - x^{2} + 3 and hence answer the following questions:

i

Does this parabola have a maximum or a minimum value?

ii

Find the minimum/maximum y-value on the graph.

iii

Describe where the axis of symmetry lies.

iv

Use technology to graph y = - x^{2} on the same axes. Describe the similarities and differences between this graph and that of y = - x^{2} + 3 in terms of the axis of symmetry and minimum/maximum values.

4

Consider the quadratic equations y = \dfrac{1}{2} x^{2} + 2 and y = \dfrac{1}{2} x^{2} - 2.

Using technology, graph the two parabolas on the same set of axes and hence answer the following questions:

a

Do these parabolas both have a minimum value or a maximum value?

b

Compare the two values of your answer in part (a). Which quadratic equation has the lower value?

c

Which parabola crosses the x-axis twice?

d

Find the x-values of the points where the parabola crosses the x-axis.

5

Consider the quadratic equations y = x^{2}, y = x^{2} - 4 x and y = x^{2} - 8 x.

Using technology, graph the three parabolas on the same set of axes and hence answer the following questions:

a

Determine whether the following statements are true or false:

i

The parabolas all cross the y-axis at different points.

ii

The parabolas all cross the x-axis twice.

iii

The parabolas all cross the y-axis at the same point.

iv

None of the parabolas cross the x-axis.

b

Compare the axis of symmetry of each parabola. Are they the same or different?

6

Using technology, graph the given pairs of functions on the same set of axes and hence answer the following questions:

i

Compare the x-intercepts of the two graphs.

ii

Do the parabolas both have maximum values, minimum values, or one of each?

iii

State the minimum/maximum y-value of the parabolas.

iv

Compare the axis of symmetry of the parabolas. Are they the same or different?

a
\begin{aligned} y &= x^{2} + 3 x - 4 \\ y &= - x^{2} - 3 x + 4 \end{aligned}
b
\begin{aligned} y &= x^{2} + x - 2 \\ y &= \dfrac{1}{5} x^{2} + \dfrac{1}{5} x - \dfrac{2}{5} \end{aligned}
Sign up to access Worksheet
Get full access to our content with a Mathspace account
Book a Demo
Sign up for free

Outcomes

MS2-12-1

uses detailed algebraic and graphical techniques to critically evaluate and construct arguments in a range of familiar and unfamiliar contexts

MS2-12-6

solves problems by representing the relationships between changing quantities in algebraic and graphical forms

What is Mathspace

About Mathspace