Ontario 10 Academic (MPM2D)
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Transformations on quadratic graphs

Interactive practice questions

Consider the function $y=2x^2$y=2x2

a

Complete the following table of values.

$x$x $-2$2 $-1$1 $0$0 $1$1 $2$2
$y$y $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
b

Plot the graph.

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c

For $y=ax^2$y=ax2, as $a$a increases, how does it change the graph of $y=x^2$y=x2?

Widens the graph

A

Narrows the graph

B

Reflects the graph across the $x$x-axis

C

Shifts the graph vertically

D

Widens the graph

A

Narrows the graph

B

Reflects the graph across the $x$x-axis

C

Shifts the graph vertically

D
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Approx 3 minutes
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This is a graph of $y=x^2$y=x2.

Consider the function $y=\left(x-6\right)^2$y=(x6)2.

This is a graph of $y=x^2$y=x2.

Outcomes

10D.QR2.01

Identify, through investigation using technology, the effect on the graph of y = x^2 of transformations by considering separately each parameter a, h, and k

10D.QR2.02

Explain the roles of a, h, and k in y = a(x – h )^2 + k, using the appropriate terminology to describe the transformations, and identify the vertex and the equation of the axis of symmetry

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