GDC skills: TI-Nspire CX
Chapter 9 / Example 4
Problems involving quadratics
A rectangular mirror has perimeter 260 cm.
a
The length of the mirror is x cm. Find the height of the mirror in terms of x.
b
Find an equation for the area of the mirror, A cm2, in terms of x.
c
Plot a graph of your equation for the area of the mirror, showing area A on the yaxis and length x on the x-axis. Choose a suitable domain and range.
d
Find the coordinates of the points where the graph intersects the x-axis.
e
State what these two values of x represent.
f
Hence find the equation of the graph’s line of symmetry.
g
State what the equation of the line of symmetry tells you in this context.
The height of the mirror is 130  x and the area a is given by
A  x 130  x  .
Open a new document and add a Graphs page.
The entry line is displayed at the top of the work area.
The default graph type is function, so ‘f1(x)=’ is displayed.
Type x  130  x  and press ·.
The x-axis will need to show values at least up to 130.
Press b 4:Window/Zoom | 1:Window Settings…
Set the axes to show 10  x  140 with an x-scale of 10 and
leave the other items as they are.
Press · when you have finished.
To makes a scale to fit the y-axis press b 4:Window/Zoom |
A:Zoom - Fit
The GDC displays the function f1(x) with suitable axes.
© Oxford University Press 2019
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GDC skills: TI-Nspire CX
Chapter 9 / Example 4
Problems involving quadratics
To find the zeros press b 6:Analyse Graph | 1:Zero
You will need to give the lower and upper bounds of the region
that includes the zero.
The GDC shows a line and asks you to set the lower bound.
Move the line using the touchpad and choose a position to the
left of the zero.
Click the touchpad.
The GDC shows another line and asks you to set the upper
bound.
Use the touchpad to move the line so that the region between
the lower and upper bounds contains the zero.
When the region contains the zero, the calculator will display
the word ‘zero’ in a box.
Click the touchpad.
The GDC displays a zero at 0, 0 .
Repeat for the second zero.
The GDC displays a zero at 130, 0 .
The x-coordinates 0 and 130 are the upper and lower limits
between which the value of x must lie.
© Oxford University Press 2019
2
GDC skills: TI-Nspire CX
Chapter 9 / Example 4
Problems involving quadratics
The equation of the line of symmetry of the graph will be at
y
0  130
or y  65 .
2
To confirm this find the vertex by pressing b 6:Analyse
Graph | 3:Maximum
You will need to give the lower and upper bounds of the region
that includes the maximum.
The GDC shows a line and asks you to set the lower bound.
Move the line using the touchpad and choose a position to the
left of the maximum.
Click the touchpad.
The GDC shows another line and asks you to set the upper
bound.
Use the touchpad to move the line so that the region between
the lower and upper bounds contains the maximum.
When the region contains the maximum, the calculator will
display the word ‘maximum’ in a box.
Click the touchpad.
The GDC displays the vertex.
The vertex of the quadratic function is at 65, 4225 .
This is the value of x, 65 cm which gives the largest area of the
mirror, 4 225 cm2.
© Oxford University Press 2019
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