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8.07 Transformations of quadratics

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.

Loading Graph...
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
Easy
2min

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

Easy
1min

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

Easy
3min

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

Easy
1min
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Outcomes

A1.6.A

Determine the domain and range of quadratic functions and represent the domain and range using inequalities

A1.6.B

Write equations of quadratic functions given the vertex and another point on the graph, write the equation in vertex form (f(x) = a(x - h)2+ k), and rewrite the equation from vertex form to standard form (f(x) = ax2+ bx + c)

A1.7.A

Graph quadratic functions on the coordinate plane and use the graph to identify key attributes, if possible, including x-intercept, y-intercept, zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry

A1.7.C

Determine the effects on the graph of the parent function f(x) = x2 when f(x) is replaced by af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d

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