SAT Function Question

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1

<p>Math whiz needed, can someone answer this:
The graph above is a parabola whose question is y = ax(squared)+2, where <code>a</code> is a constant. If y=a/3x(squared)+2 is graphed on the same axes which of the following best describes the resulting graph as compared with the graph above?
a. it will be narrower
b. it will be wider
c. it will be moved to the left
d. it will be moved to the right
e. it will be moved 3 units downward</p>

<p>answer:b<br>
source: sat blue book pg 465, test 2 section 5 #7
thank you for your time</p>

2

<p><a href=“http://www.math.utah.edu/online/1010/parabolas/prob/parabola.gif[/url]”>http://www.math.utah.edu/online/1010/parabolas/prob/parabola.gif&lt;/a&gt; the parabola looks likethis except its movedliked three units up</p>

3

<p>Cheesydonut, </p>

<p>I do not have the Blue Book with me at the moment but I will try to help you. First, I must assume that the second equation should be written as y = (a/3)x^2, in other words, the x^2 is not in the denominator. The coefficient that multiplies the x^2 determines the width of the parabola. A fractional coefficient (less than one) always makes the parabola rise more slowly thus making the graph wider. Similarly, a coefficient greater than one will make the parabola narrower</p>

4

<p>Maths whizz reporting for duty</p>

<p>Basically you the answer so you want to know why it is correct.
c,d,e cannot be right because the gradient does not make it move anywhere
a and b however are the only thing that will be effected
basically the lower the gradient the wider it will be
since a which is the gradient is divided by 3 the graph will become wider</p>

5

<ul>
<li>Solution by picking a number and graphing: Let’s pick a value for a, say a = 3. Then the given graph is for the equation y = 3x^2 + 2, and the equation for the graph not shown is y = x^2 + 2. Now put both of these into your graphing calculator by pressing the Y= button and typing the following for Y1 and Y2.</li>
</ul>

<p>Y1 = 3x^2 + 2
Y2 = x^2 + 2</p>

<p>Then press ZOOM 6 to graph these in a standard viewing window. Make sure you watch carefully as these are drawn. Y1 will be drawn first, followed by Y2. Note that the second one drawn is wider than the first. Therefore the answer is choice (B).</p>

6

<p>A quick lesson in transformations: Given a function f(x) and a positive number c, we have the following basic transformations.</p>

<p>f(x) + c vertical shift up c units
f(x) – c vertical shift down c units
f(x – c) horizontal shift right c units
f(x + c) horizontal shift left c units</p>

<p>-f(x) reflection in x-axis
f(-x) reflection in y-axis</p>

<p>cf(x) vertical expansion if c > 1, vertical compression if 0 < c < 1
f(cx) horizontal expansion if 0 < c < 1, horizontal compression if c > 1</p>

<p>Solution using a transformation: In the given question we have a horizontal expansion. To see this is a bit tricky. Let f(x) = ax^2 + 2. Then the second equation is </p>

<p>y = (a/3) x^2 + 2 = a(1/√3 x)^2 + 2 = f(1/√3 x)</p>

<p>Since 1/√3 < 1 we see that this is a horizontal expansion. In other words, the graph will be wider.</p>

7

<p>@Cheesydonut, the coefficient of x got smaller but still +ve , so the graph got wider…
That’s what I know! :smiley:
Like if a were 7 then became 3, the graph will get wider… Not necessary from 1 to between 1 and zero like someone said i guess…</p>

<p>a= multiply or divide "a"by +ve and "a"becomes a bigger nb, narrower graph
a= multiply or divide "a"by +ve and "a"becomes a smaller nb, wider graph
a= multiply or divide "a"by negative, the graph is reflected…
:D</p>

<p>drsteve,
“cf(x) vertical expansion if c > 1, vertical compression if 0 < c < 1”
u mean… vertical expansion= get narrower…
vertical compression= get wider
?!?!</p>