NOTES: GRAPHING QUADRATIC FUNCTIONS DAY 2 Textbook Chapters: 4.2, 6.5

OBJECTIVE: Today you will learn how to graph quadratic functions!

Parent Function: y = x2 General Form: y = a (x – h)2 + k

1. Vertex: ( , )

x y

2. y = 2(x + 3)2 − 8

Vertex: ( , ) Chart

YOU TRY: 1. y = 3(x – 2)2 – 3 2. y = –

12 (x – 4)2 + 5

5. Graph: y = –2(x + 2)2 + 2 6. Is the inverse of #5 a function? Graph the inverse of #5. Domain: _____________________ Domain: _____________________

Range: _______________________ Range: _______________________

Increasing: ____________________ Increasing: ____________________

Decreasing: ___________________ Decreasing: ___________________

Zeroes: _______________________ Zeroes: _______________________

Y-intercept: ___________________ Y-intercept: ___________________

As x →∞, f (x )→ ____ As x →∞, f (x )→ ____ As x →−∞, f (x )→ ____ As x →−∞, f (x )→ ____ Solve using the SQUARE ROOTS METHOD. 1. (2x + 5)2 – 12 = 0 2. 4(x – 1)2 – 200 = 0

PRACTICE: GRAPHING QUADRATIC FUNCTIONS DAY 2 Function Direction Dilation Horizontal Shift Vertical Shift Vertex

1 y = − | x +10 |−3 Up Down

Stretch Shrink None

Left/Right: _____ Left/Right: _____ ( , )

2 y =−100|x|+2 Up Down

Stretch Shrink None

Left/Right: _____ Left/Right: _____ ( , )

3 y = 4(x +1)2 − 2 Up

Down

Stretch Shrink None

Left/Right: _____ Left/Right: _____ ( , )

4 y = 5

3x2 −1

Up Down

Stretch Shrink None

Left/Right: _____ Left/Right: _____ ( , )

1) f (x) = − x +1( )2

+ 4 Vertex: ( , )

2) f (x) = 2 x + 4( )2

− 3

Vertex: ( , )

3) f (x) = −3 x +1( )2

Vertex: ( , )

4) f (x) = −2x2 + 5

Vertex: ( , )

CALCULATOR PRACTICE: Round to 2 decimal places 1. Graph: y = 2x2 + 3x – 3 Relative Minimum(s): ___________ Zeroes: _______________________ Domain: ______________________ Range: _______________________ Y-Intercept: ___________________

2. Graph: y = 1

2x 2 +5x +3

Vertex: _______________________ Zeroes: _______________________ Y-Intercept: ___________________ Intervals of Increasing: ________________ Intervals of Decreasing: _______________

2. Circle at all the equations that have the same domain as: y = x 2 +3 y = |x| y = x3 + 4 y = x y = x y = x3 y = 2 4. 5. Throughout which of the following

intervals is f(x) = (x – 1) (x – 4)2 only decreasing?

NAME: _______________________________ ___ DAY 1 DUE: _______

1) f (x) = − x − 2( )2

+ 4 Vertex: ( , )

2) f (x) = 2 x + 5( )2

−1

Vertex: ( , )

3) f (x) = − 1

2x2 Vertex: ( , )

4) y = 2 | x +1|−3 Vertex: ( , )

5) f (x) = −3 x − 2( )2

Vertex: ( , )

6) f (x) = 2x2 − 8

Vertex: ( , )

7. Write a quadratic equation and an absolute value equation with the same range.

8. Circle all the functions that have a range of: y ≤ 4 y = x2 + 4 y = –|x – 1| + 4 y = –x2 + 4 y = –(x + 4)2

Fill out the table.

Function Direction Dilation Horizontal Shift Vertical Shift Vertex

9 y = − 1

4| x +1|−5

Up Down

Stretch Shrink None

Left/Right: _____ Left/Right: _____

( , )

10 y = 9(x + 5)2 −1 Up

Down

Stretch Shrink None

Left/Right: _____ Left/Right: _____

( , )

11 y = 1

2(x +1)2

Up Down

Stretch Shrink None

Left/Right: _____ Left/Right: _____

( , )

12 y =|x|+2 Up Down

Stretch Shrink None

Left/Right: _____ Left/Right: _____

( , )

Solve the quadratic equations using the SQUARE ROOTS METHOD! 1. –2x2 = –162 2. 3x2 – 15 = 57

3. 5x2 – 3 = 97 4. 4x2 + 5 = 6

5. 9x2 – 16 = 9 6. 2x2 – 7x = 15 (hint: factor!)