# Graphing Functions

Algebra: Graphing Functions:

Read the following SAT test question and then select the correct answer.

Always use the Knowsys Method on all math questions. This will help you think systematically and avoid careless mistakes. First, read the entire question carefully. Identify the bottom line and note it at the top of your scratch work. Next assess your options: What could I do? What should I do? Choose the most efficient method to attack the problem, and loop back to make sure that your answer matches the bottom line you were looking for.

$y=-2x^{2}+bx+5$

In the xy-plane, the graph of the equation above assumes its maximum value at x = 2. What is the value of b?

First, consider your bottom line. "What is the value of b?" At the top of your scratch work, write b = ?

Next, start assessing your options. What does it mean that the chart "assumes its maximum" at x = 2? Look at all the parts of the function. The highest power is 2, so you know that this is a quadratic function and that the chart will have a parabola. Since the coefficient of that variable is -2, you also know that the parabola will open downward. If the graph's maximum value is located at x = 2, you know that the vertex of the parabola will be somewhere to the right of the origin, on the vertical line two spaces to the right of the y-axis.

What can you do with that knowledge? Think about how you can move a parabola to the right of the origin. You might remember the formula $f(x - h)^{2}+k$. If you've forgotten, the point (h, k) represents the vertex of the parabola. You need to combine this with the function you were originally given.

$y=-2(x - 2)^{2}+5+k$

Next, use FOIL and the Distributive Property to square the binomial (x - 2) and multiply in the coefficient.

$y=-2x^{2}+8x-8+5+k$

At this point, you should stop and double-check your bottom line. You don't need to worry about solving for k, x, or y because you have already solved what your bottom line was asking: the value of b. Always keep your bottom line in mind so you remember to loop back and so you can be sure you answer what was asked.

Now that you know that b = 8, look at the answer choices:

(A) -8
(B) -4
(C) 4
(D) 8
(E) 10