Download Standard to Vertex: Using algebraic methods to find exact answers

11.13.08 Lesson: The Story of Quadratics Continued
At the end of the day students will…
Be able to solve a quadratic function given in standard form.
Standards Taught
Identify quadratic patterns
Solving quadratic functions for x or y values, write quadratic functions given a contextual
situation
Discriminate between linear, exponential, and quadratic patterns.
Anticipation of next steps…
Discriminate between linear, exponential, and quadratic patterns
Solving quadratic functions for x or y values, write quadratic functions given a contextual
situation
Warm-Up…
Four tables of values, 2 linear, one exponential and one quadratic
x
-2
-1
0
1
2
3
4
y
21
11
5
3
5
11
21
x
3
8
9
14
17
20
25
y
7
17
19
29
35
41
51
x
16
19
21
25
35
37
41
y
3.417
3.5004
3.556
3.6672
3.9452
4.0008
4.112
x
0
5
9
11
15
25
36
y
10
13.132
16.33
18.21
22.644
39.048
71.105
Calculator Tip: Yet another way to check your work! Change the table to Independent
ask to verify the exact table.
Step by Step Instruction…
1. Test corrections (15 minutes)
2. Debrief yesterday’s work Q&A(10 minutes)
3. Direct Instruction – Converting to vertex form from standard form. (20 minutes)
Solve graphically (Each problem increases in difficulty because the landmarks are not
shown in the last problem.
9  x2  4 x  8
What if the graph doesn’t show all the landmarks?
110   x 2  10 x  100
What if the graph doesn’t show any of the landmarks?
 x 2  5 x  300  294
Solve Algebraically by converting forms. Use the three problems above.
Get to the table
.
5. Using Algebraic methods to find exact answers worksheet (20 minutes)
Independent Practice…
Name:
Standard to Vertex: Using algebraic methods to find exact answers
Complete each table and write each quadratic function in vertex form, y  A  R( x  w)2 .
y  x 2  10 x  15
1
y   x2  6 x  10
2
3
0
1
2
3
4
5
-8
-7
-6
-5
-4
-3
y  3x 2  12 x  6
-5
-4
-3
-2
-1
0
Vertex form
Vertex form
Vertex form
________________
________________
________________
Write each quadratic function in vertex form and then use inverse in reverse to find the
exact input for the given output.
4
y  x 2  6 x  18
5
 x2  9 x  8  y
6
h(t )  4t 2  16t  20
Vertex form
Vertex form
Vertex form
________________
________________
________________
Find x if y = 100
Show all your work!
Find x if y = 0
Find t if h(t) = 0
7
A potato is shot from a potato gun and its height (feet) is a function of time (seconds)
given by the function: h(t )  16t 2  64t  50
a) Fill in this chart so that it shows the
vertex and write the function in vertex form.
b) How long is the potato in the air?
c) What is the maximum height reached by the potato?
d) When will the potato be 20 feet in the air?
e) After 3.5 seconds, how high is the potato?