Help With Math Question From Blue Book!!

Test Preparation SAT Preparation
1

<p>Hey guys--</p>

<p>I was just wondering if anyone could help me with a question in the College Board Official SAT preparation book. For those of you who have it, you know that there are no answer explanations. As a result, I must result to the genius minds at college confidential!!</p>

<p>The figure above shows the graphs of y=x^2 and y=a-x^2 for some constant a. IF the length of PQ is equal to 6, what is the value of a?</p>

<p>The question is Number 15, Section 9, First Practice Test.</p>

<p>It's a graphing question, so I won't be able to write it in full detail.</p>

<p>For all of you who have the book, please look it up, and explain it to me.</p>

<p>Thanks!!!</p>

2

<p>The answer is (E) 18 btw.</p>

3

<p>since pq = 6 you can obtain the y value for that point because its bisected by the y axis. i dont have the book on me now, but you basically plug in the x value 3, yielding y=9. and then plug in a x and y to the second equation since they share a common point. 9=a-(3)^2 = 18</p>

4

<p>thanks alot hoopsplaya...everything's so obvious after you figure it out. =p</p>

5

<p>Hoopslaya238 gave the right solution.</p>

<p>But hpn1491, your question was already answered.
Look for 427 / 15 in [url=<a href="http://talk.collegeconfidential.com/showthread.php?t=339734%5DConsolidated"&gt;http://talk.collegeconfidential.com/showthread.php?t=339734]Consolidated&lt;/a> List of Blue Book Math Solutions, 3rd ed.<a href="the%20second%20link%20for%20427%20/%2015%20is%20redundant">/url</a>.</p>

<p>The ending can be done different.</p>

<h1>The same beginning:</h1>

<p>If PQ intersects the y-axis in R.
RQ = PQ /2 = 6/2 = 3.
For y = x^2
y(3) = 3^2 = 9 -> Q(3,9)</p>

<h1>Now different:</h1>

<p>Q(3,9) -> OR = 9.
If y = a - x^2 intersects the y-axis in S,
a is y-intercept, a = OS = (2) OR = (2)9 = 18,
since points O and S are symmetric about PQ.</p>

6

<p>Let me make it more vivid.</p>

<p>Let M is the intersect point of PQ and y-axis and Px, Qx are respectively the abscissas of the point P and Q.
=> Px, Qx are root of: x^2 - (a-x^2)=0 <=> 2x^2-a=0
=> Px + Qx = 0 => P and Q are symmetric across y-axis => PM = QM = PQ/2 = 3
Furthermore, y-axis is the symmetric axis of y=x^2
=> PQ // x-axis => Px = PM = 3 => Py = 9. Here, the rest is obvious. </p>

<p>P/s: I've done these above 'cos Hoopsplaya238 might assume that PQ//Ox. Still, sometimes "figures not drawn to scale"</p>