mm2a3c investigate and explain characteristics of quadratic function, including domain, range,...

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


M2 Unit 1B: Day 4


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


M2 Unit 1B: Day 4


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


M2 Unit 1B: Day 4


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.


M2 Unit 1B: Day 4


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.


M2 Unit 1B: Day 4


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!


M2 Unit 1B: Day 4


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.


M2 Unit 1B: Day 4


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


M2 Unit 1B: Day 4


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


M2 Unit 1B: Day 4


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


M2 Unit 1B: Day 4


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


M2 Unit 1B: Day 4


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 !


M2 Unit 1B: Day 4


13

THE END

HOMEWORK:Day 4 Handout

mm2a3c investigate and explain characteristics of quadratic function, including domain, range,...

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