# Algebra Functions

#### This means that when y or f(x)=0, then x is both 3 and –4. Those are the x-intercepts.

Quadratic equations  (ƒ(x) = ax2 +b x -c) are always in the shape of a parabola.  Here’s some things to remember about the equation:

• If the value of a is positive the parabola opens up
• If the value of a is negative the parabola opens down
• The greater the value of a, the greater the slope and the narrower the parabola
• The maximum/minimum is the high/low point of the parabola (vertex)
• The x-coordinate of the vertex equals -b/2a
• The y-coordinate of the vertex equals (b2-4ac)/4a
• ƒ(x) = a(x-h)2 +k is referred to as the vertex form where h and k are the x- and y-coordinates respectively.

Reflections of a Function

#### Here’s the way you probably saw this issue described in your algebra class:

If y = f(x), then
y = f(−x) is its reflection about the y-axis,
y = −f(x) is its reflection about the x-axis.

## Sample Questions

5.  The graph of which of the following equations is perpendicular to the graph of 2y = 2x + 1?

(A) y + x = 7
(B) 2y – 2x = 1
(C) 2y = x + 1
(D) y = x + .5
(E) 2y = 2x + 2

6.  What are the (x,y) coordinates of the unique point on the graph of 2x + 3y = -9 when y = -5?

(A) -5, 3
(B) -5, 0
(C) 2, -5
(D) 3, -5
(E) 3, 5

15.  Which of the following functions most closely represents the graph above?

(A) f(x) = x2 +3
(B) f(x) = (x2 – 3) -1
(C) f(x+3) = x2 – 1
(D) f(x) = x2-1
(E) f(x) = (x + 3)2 + 1