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MM2A3c Investigate and explain characteristics of quadratic function, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals of increase and decrease, and rates of change.
M2 Unit 1B: Day 4
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
1
Write the expression as a complex number in standard form.
1. (3 2 ) (5 7 )i i
2. (10 3 )(10 3 )i i
3. 3 (8 5 )i i
4. Find the absolute value of the complex number.
3 i5. Plot the complex number in a complex plane.
i72
)15 24A i 2)15 24B i i) 15 24C i ) 15 24D i )15 24E i
Review/Preview (Unit 1A) #3
MM2A3c Investigate and explain characteristics of quadratic function, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals of increase and decrease, and rates of change.
M2 Unit 1B: Day 4
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
2
Write the expression as a complex number in standard form.
1. (3 2 ) (5 7 )i i
2. (10 3 )(10 3 )i i
3. 3 (8 5 )i i
4. Find the absolute value of the complex number.
3 i5. Plot the complex number in a complex plane.
i72
)15 24A i 2)15 24B i i) 15 24C i ) 15 24D i )15 24E i
8 9i
109
A
4
Review/Preview (Unit 1A) #3
MM2A3c Investigate and explain characteristics of quadratic function, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals of increase and decrease, and rates of change.
M2 Unit 1B: Day 4
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
3
Lesson 3.2
Tuesday, April 18, 2023
Review of Quadratic Review of Quadratic FunctionsFunctions
EQ: How do we graph a quadratic EQ: How do we graph a quadratic function?function?
M2 Unit 1B: Day 4
MM2A3c Investigate and explain characteristics of quadratic function, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals of increase and decrease, and rates of change.
M2 Unit 1B: Day 4
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
What is the standard form of a quadratic function.
Quadratic Functions
4
2( )f x a x h k
Standard Form
Vertex Form
2( ) f x ax bx c
What is the vertex form of a quadratic function.
MM2A3c Investigate and explain characteristics of quadratic function, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals of increase and decrease, and rates of change.
M2 Unit 1B: Day 4
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
5
How do we find the axis of symmetry and vertex if we know the vertex form?
2( )f x a x h k Vertex Form
We use to find the axis of symmetry. 2
bx
a
Then we substitute this value into the equation and to find the y-coordinate for the vertex.
MM2A3c Investigate and explain characteristics of quadratic function, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals of increase and decrease, and rates of change.
M2 Unit 1B: Day 4
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
6
Standard Form2( ) f x ax bx c
How do we find the y-intercept?
We identity “c”. It is always the y-intercept if theequation is in standard form!
MM2A3c Investigate and explain characteristics of quadratic function, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals of increase and decrease, and rates of change.
M2 Unit 1B: Day 4
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
7
How do we find the y-intercept?
2( )f x a x h k Vertex Form
We substitute “zero” for the x-coordinate solve for f(x) or y.
MM2A3c Investigate and explain characteristics of quadratic function, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals of increase and decrease, and rates of change.
M2 Unit 1B: Day 4
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
Vertex:
Y-intercept:
Axis of symmetry:
One more point:
Domain:
Range:
Max or Min?
Graph. 1x
1, 1
0, 4
2, 4
maximum
All real numbers
h = -1 k = -1
21. ( ) 3 1 1f x x
1y
MM2A3c Investigate and explain characteristics of quadratic function, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals of increase and decrease, and rates of change.
M2 Unit 1B: Day 4
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
Vertex:
Y-intercept:
Axis of symmetry:
One more point:
Domain:
Range:
Max or Min?
Graph. 3
2x
3 17,
2 4
0, 11
3, 11
maximum
All real numbers
9
17
4y
22. ( ) 3 9 1f x x x
9
2 3x
2
bx
a
MM2A3c Investigate and explain characteristics of quadratic function, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals of increase and decrease, and rates of change.
M2 Unit 1B: Day 4
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
Vertex:
Y-intercept:
Axis of symmetry:
One more point:
Domain:
Range:
Max or Min?
Graph. 1
2x
1 9,
2 4 0,2
1,2
maximum
All real numbers
10
9
4y
2( ) 2 2f x x x x
1
2 1x
2
bx
a
3. ( ) 2 1f x x x
2( ) 2f x x x 2( ) 2f x x x
You can use the original factor to get two more points!
2 0 1 0x x +2 +2
2x 1 1
1x
MM2A3c Investigate and explain characteristics of quadratic function, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals of increase and decrease, and rates of change.
M2 Unit 1B: Day 4
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
11
Converting forms 2
4. ( ) 3 1 1f x x 25. ( ) 3 9 1f x x x
( ) 3 1 1 1f x x x
2( ) 3 2 1 1f x x x
2( ) 3 6 3 1f x x x
2( ) 3 6 4f x x x
3a
9 3
2 2( 3) 2
bx
a
3 23: ( , )
2 4vertex
23 33( ) 9( ) 1
2 223
4
y
y
2( )f x a x h k
23 23
( ) 32 4
f x x
MM2A3c Investigate and explain characteristics of quadratic function, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals of increase and decrease, and rates of change.
M2 Unit 1B: Day 4
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
12
Find the minimum or maximum value of the function.
6. 2 6y x x 22 12y x x
123
2 2(2)
bx
a
22 3 12 3y
18y The minimum value of the function is the y-coordinate of the vertex!
This parabola will have a minimum !
MM2A3c Investigate and explain characteristics of quadratic function, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals of increase and decrease, and rates of change.
M2 Unit 1B: Day 4
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
13
THE END
HOMEWORK:Day 4 Handout