CollegeBoard SAT Question of the Day Help?

Test Preparation SAT Preparation
1

<p>Can someone give me a hint about how to do the question? Not the answer choice, but give me a hand or two? Thanks. </p>

<p>Its:</p>

<p>y=-2x^2+bx+5</p>

<p>In the xy-plane, the graph of the equation above assumes its maximum value at . What is the value of b?</p>

<p>a) -8
b) -4
c) 4
d) 8
e) 10</p>

2

<p>use the vertex formula</p>

3

<p>You can solve this either by [using</a> the forumla](<a href=“http://www.algebra-class.com/vertex-formula.html]using”>Using the Vertex Formula-Quadratic Functions) or by [url=&lt;a href=“http://www.purplemath.com/modules/sqrvertx.htm]completing”&gt;Squaring to Find a Parabola's Vertex - Explained! | Purplemath]completing</a> the square<a href=“which%20is%20really%20the%20same%20thing,%20since%20the%20vertex%20formula%20can%20be%20%5Burl=http://www.purplemath.com/modules/sqrvertx2.htm]derived%20by%20completing%20the%20square[/url]”>/url</a>.</p>

4

<p>I got it right! Thanks :)</p>

5

<p>Or… graph it on a graphing calculator and adjust as needed. Took me ~45 seconds.</p>

6

<p>Cool, I guess?</p>

7

<p>Lol, used calculus, first time incorporating calculus into the SAT.</p>

8

<p>Ehh, by calculus do you mean by finding the second derivative? Too much work, especially when you can take 5 seconds to graph it on your calculator :P</p>

9

<p>Or you could just use the axis of symmetry formula. The axis of symmetry formula is derived through calculus.</p>

<p>Simply:
Axis of Symmetry formula: x = -b/(2a)
2 = -b/(-4)
2 = b/4
8 = b</p>

<p>Proof of the Axis of Symmetry formula:
f(x) = ax^2 + bx + c
f’(x) = 2ax + b
0 = 2ax + b
-b/(2a) = x</p>

<p>We can transform that into
b = -2ax
or
a = -b/(2x)</p>

<p>We used the top one.</p>

10

<p>No, a maximum of a function is when the derivative equals 0, so just set the derivative to 0.</p>