Name: ______Date: ______

Mr. Art Period: ______

Graphing Quadratic Functions (Parabolas), Linear-Quadratic Systems, Absolute Value Functions, and Exponential Functions

I. Graphing Quadratic Functions (Parabolas)

1) Standard form y = ax2 + bx + c

à

2) Y-intercept: c from the equation

·  x-value equals 0

·  the point (0,c) à (0, -3)

3) Vertex or Turning Point

·  parabolas are symmetrical

·  the point where a parabola changes direction

·  Look for the pattern in the table à (1, -4)

4) Axis of Symmetry or Line of Reflection

·  the vertical line that cuts the parabola in half

·  the vertical line that cuts through the vertex

·  x-value of vertex or turning point

·  à

5) Concave Up or Concave Down?

·  Positive a (from equation)

·  looks like a "U" (concave up) & has a minimum point

·  +a (good mood)...smiley face

·  Negative a (from equation)

·  looks like a "" (concave down) & has a maximum point

·  –a (sad mood)...frowning face

6) Narrow or Wide?

·  as a increases, the parabola becomes narrower

·  as a decreases, the parabola becomes wider

7) Roots or Solution Set: the solutions of a quadratic equation

·  point(s) where the parabola intersects the x–axis

·  y-values equal 0

·  Braces around the point(s) or only around the x-values

8) Arrows or No Arrows?

·  given Domain or Interval à NO arrows on parabola

·  No given Domain or Interval à Arrows on parabola

II. Graphing Linear-Quadratic Systems

x / y
-5 / 6
-4 / 1
-3 / -2
-2 / -3
-1 / -2
0 / 1
1 / 6
x / y
-5 / -9
-4 / -7
-3 / -5
-2 / -3
-1 / -1
0 / 1
1 / 3

III. Absolute Value Functions

1) y = | x | is the graph of (opens upward, like a parabola with +a value)

2) y = - | x | is the graph of (opens downward, like a parabola with -a value)

3) y = 2| x | is the graph of y = | x | but narrower (as a increases, the graph gets narrower, like a parabola)

4) y = 0.5| x | or y =| x | is the graph of y = | x | but wider (as a decreases, the graph gets wider, like a parabola)

5) y = | x | + 2 is the graph of y = | x | translated UP "2" units

6) y = | x | - 2 is the graph of y = | x | translated DOWN "2" units

7) y = | x + 2 | is the graph of y = | x | translated LEFT "2" units

8) y = | x - 2 | is the graph of y = | x | translated RIGHT "2" units

IV. Exponential Functions à y = abx

1) y = 2x à when the base is greater than 1, the graph curves upward (exponential growth)

2) y = or y = à when the base is a positive decimal or fraction,

the graph curves downward (exponential decay)

3) Exponential growth and decay graphs have the point (0,1) in common because and number,.

4) As the base (b) increases, the graph becomes steeper faster

As the base (b) decreases, the graph flattens out.

5) y = 2-x is the graph y = 2x reflected over the y-axis

y = 2-x is the same graph as y = because a negative exponent is the same as a fraction

6) y = -2x is the graph y = 2x reflected over the x-axis

V. Exponential Growth & Decay Word Problems

* Formula is not on Reference Sheet à Must be memorized!

1)

2)

VI. Functions

1) Relation - set of ordered pairs à{(1,3), (4,7), (-2,6), (5,2)}

2) Domain - the set of all first elements of the ordered pairs in a relation (x-values) à Domain: {1, 4, -2, 5}

3) Range - the set of all second elements of the ordered pairs (y-values) à Range: {3, 7, 6, 2}

4) Function - a relation in which no two ordered pairs have the same first element (x-values)

a) Is the following relation a function? b) Is the following relation a function?

{(1,3), (4,7), (-2,6), (5,2)} {(1,3), (4,7), (-2,6), (4,2)}

YES! because all x-values are different! NO! because the x-value 4 repeats!

c) Which table of values represents a function?

d) Which table of values represents a function?

e) f (x) = 5x - 11, find f (3) à This simply means to plug x into the function and find y.

4