Grade 12

Mixed Graphs III (quad, exp, cubic, 1/x)

Lesson

Practice

Lesson

Worked Examples

question 1

Consider the quadratic function $y=-2x^2+16x-24$y=−2x2+16x−24.

Determine the $x$x-value(s) of the $x$x-intercept(s) of this parabola. Write all answers on the same line separated by commas.
Determine the $y$y-value of the $y$y-intercept for this parabola.
Determine the equation of the vertical axis of symmetry for this parabola.
Find the $y$y-coordinate of the vertex of the parabola.
Which of the following is a graph of the parabola $y=-2x^2+16x-24$y=−2x2+16x−24?
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A
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B
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C
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D

QUESTION 2

To minimise the chance of large avalanches, small explosives are fired onto mountain sides. One such explosive is fired at a height of $24$24 metres and follows a parabolic flight path. It reaches a maximum height of $122$122 metres, $180$180 metres horizontally from where it is fired.

Let $x$x and $y$y represent the horizontal and vertical distances of the explosive from where it is fired. Assuming the position where it is fired is $\left(0,0\right)$(0,0), determine the vertex of the parabolic path, in the form $\left(x,y\right)$(x,y).
Using the form of the parabola $y=-a\left(x-h\right)^2+k$y=−a(x−h)2+k, determine the exact value of $a$a. Then use this value to determine the equation between $x$x and $y$y.
The explosive hits a slope that is $361$361 metres horizontally from the point where it was fired. Does the explosive land above, at the same height or below the point where it was fired?
$At the same height$
A
$Above$
B
$Below$
C

QUESTION 3

Consider the table of values.

number of days passed ($x$`x`)	$1$1	$2$2	$3$3	$4$4	$5$5
population of $shrimp$ ($y$`y`)	$5$5	$25$25	$125$125	$625$625	$3125$3125

number of days passed ($x$`x`)	$1$1	$2$2	$3$3	$4$4	$5$5
population of $shrimp$ ($y$`y`)	$5$5	$25$25	$125$125	$625$625	$3125$3125

Is the number of $shrimp$ increasing by the same amount each day?
Yes
A
No
B
Find the equation linking population $y$y and time $x$x in the form $y=a^x$y=ax.
Graph the equation.

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QUESTION 4

Consider the cubic function $y=2x^3+2$y=2x3+2

Is the cubic increasing or decreasing from left to right?
Increasing
A
Decreasing
B
Is the cubic more or less steep than the cubic $y=x^3$y=x3 ?
More steep
A
Less steep
B
What are the coordinates of the point of inflection of the cubic?

Inflection ($\editable{}$, $\editable{}$)
Plot the graph $y=2x^3+2$y=2x3+2

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QUESTION 5

Consider the function $y=\frac{3}{x}+3$y=3x+3

Which of the following indicates the position of the hyperbola's branches relative to its asymptotes?

A

B
Which curve approaches positive and negative infinity more quickly, $y=\frac{1}{x}$y=1x or $y=\frac{3}{x}+3$y=3x+3?
$y=\frac{3}{x}+3$y=3x+3
A
$y=\frac{1}{x}$y=1x
B
What are the equations of the vertical and horizontal asymptotes?

Vertical asymptote $x$x= $\editable{}$

Horizontal asymptote $y$y= $\editable{}$
Plot the graph $y=\frac{3}{x}+3$y=3x+3

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