Transcript Algebra 2 Name: 4.4 Investigation

Comparing Characteristics of
Quadratic Functions

Essential Questions:

How do you compare two quadratic
functions?
Warm-Up 3 (2.27.2014)
1. Find the zeros, find the maximum or
minimum, y-intercept, axis of symmetry,
then sketch the graphs.
A.
x2 – x – 20 = 0
B.
x2 + 8x + 15 = 0
CCM 2
Name:
Round 1: Projectiles and Parabolas
Look at the two trajectories above.
1. What is the same about the two equations?
2. What does the y-intercept represent? What part of the equation gives you the yintercept?
3. What do the x-intercepts represent?
4. The highest part of the bird’s flight is represented by what part of the parabola?
5. A. How far does Angry Bird fly in h(x)?
B. How high does he go?
C. How far away from the catapult is he when he is at his highest?
D. When he is 15 feet away, how high is he flying?
Characteristics (or Extrema ) of Quadratics:
•X-intercepts
•the zeros or solutions of the quadratic
•Y-intercept
•when x=0
•where the quadratic crosses the y-axis)
•Minimum or Maximum
•the Vertex
• the x-value of the vertex is the average of the zeros
•Axis of symmetry (NEW)
•The line the parabola is reflected over
•Will always be an “x = #” line
•Always the line “x = the x-value of the
vertex”
b
•Another way to fins this is x 
2a
•use this way if you cannot easily factor
the quadratic

Round 2
1. When Angry Bird is 9 feet away, how high is he flying?
2. The axis of symmetry is provided.
A. What part of the parabola does this pass through?
B. What does this part represent about Angry Bird’s flight?
3. How high does the bird fly?
4. Reflect points over the axis of symmetry to complete the parabola. Do you hit any
pigs?
5. How far would Angry Bird fly if he did not hit any obstacles?
6. Without solving for the whole equation,
A. What is “c” value in standard form?
B. Is “a” positive or negative?
Round 3
1. Angry bird is at (0,0). Angry bird and hungry pig are 18 feet away from each other. If
angry bird and hungry pig are at the same height (y-value) when angry bird is
catapulted, at what distance away is Angry Bird the highest? Hint: Think about
symmetry.
2. Angry Bird wants to hit the pig on the right. The equation representing his flight is:
y   . 083 x  1 . 82 x  0
2
A. Using the picture, what is the y-intercept?
B. Using the picture, what are the x-intercepts?
C. Where is the axis of symmetry? You may use the picture to visualize, but
show your algebraic work using:
Round to the nearest integer.
b
x 

2a
D. How high does Angry Bird fly (rounded to the nearest integer)?
E. Sketch the graph of Angry Bird’s flight.
Comparing Quadratics of different forms.
•An equation (You can covert this to a graph)
•A graph
•A table (You can find the quadratic regression line, then graph)
Black Bird
Black Bird’s flight path can be modeled by the quadratic
equation y   x 2  28 x  171
Maximum Height________
Axis of Symmetry_________
Distance Traveled: ____________
Red Bird
Red Bird’s flight is represented by the graph:
Maximum Height________
Axis of Symmetry_________
Distance Traveled: ____________
Blue Bird
The table below contains data points of Blue Birds flight
trajectory.
X 2 3 4 5 6 7 8 9 10
y
0
9
16
Maximum Height________
21 24
25
24
21
16
Axis of Symmetry_________
Distance Traveled: ____________
Complete Angry Birds Part 2
for Class Work
Exit Ticket
1.
2.
3.
4.
5.
6.
Can you multiply binomials?
Can you factor when a = 1?
Can you factor when a is NOT 1?
Can you find the vertex?
Can you find the y-intercept?
Can you write a quadratic equation given any condition?
HW: