Quadratic Relations

Ontario 10 Academic (MPM2D)

Transformations on quadratic graphs

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

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`=`a``x`2, as $a$`a` increases, how does it change the graph of $y=x^2$`y`=`x`2?

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

Easy

Approx 3 minutes

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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

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