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How do you find and use the vertex?. How do you find and use the vertex ?. Review. What is a quadratic function (relationship)?. A function in which the input is squared. Review. What are the ‘forms’ of linear functions?. Standard. Slope-Intercept. Y = mX + b. AX + BY = C. NEW.

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Presentation Transcript
slide3

Review

What is a quadratic function (relationship)?

A function in which the input is squared

slide4

Review

What are the ‘forms’ of linear functions?

Standard

Slope-Intercept

Y = mX + b

AX + BY = C

NEW

Quadratic function standard form:

use case vertical motion model

Use Case: Vertical Motion Model

Big question about timeand height?

As seconds increase,

what happens to feet?

slide6

Suppose I shoot a bb straight up. It leaves my gun 6 feet above the ground, traveling at 50 feet per second. How much time will it take for the bb to get to its maximum height (nearest hundredth)?

FEET

Sketch?

SECONDS

slide7

Suppose I shoot a bb straight up. It leaves my gun 6 feet above the ground, traveling at 50 feet per second. How much time will it take for the bb to get to its maximum height (nearest hundredth)?

FEET

(?, ?)

SECONDS

slide8

Suppose I shoot a bb straight up. It leaves my gun 6 feet above the ground, traveling at 50 feet per second. How much time will it take for the bb to get to its maximum height (nearest hundredth)?

Rule?

FEET

(?, ?)

SECONDS

slide9

Suppose I shoot a bb straight up. It leaves my gun 6 feet above the ground, traveling at 50 feet per second. How much time will it take for the bb to get to its maximum height (nearest hundredth)?

FEET

(?, ?)

SECONDS

slide10

Suppose I shoot a bb straight up. It leaves my gun 6 feet above the ground, traveling at 50 feet per second. How much time will it take for the bb to get to its maximum height (nearest hundredth)?

FEET

Sec.

Ft.

(?, ?)

SECONDS

slide11

Suppose I shoot a bb straight up. It leaves my gun 6 feet above the ground, traveling at 50 feet per second. How much time will it take for the bb to get to its maximum height (nearest hundredth)?

FEET

Sec.

Ft.

(?, ?)

SECONDS

slide12

Suppose I shoot a bb straight up. It leaves my gun 6 feet above the ground, traveling at 50 feet per second. How much time will it take for the bb to get to its maximum height (nearest hundredth)?

FEET

Sec.

Ft.

(?, ?)

(0, 6)

SECONDS

slide13

Suppose I shoot a bb straight up. It leaves my gun 6 feet above the ground, traveling at 50 feet per second. How much time will it take for the bb to get to its maximum height (nearest hundredth)?

FEET

Sec.

Ft.

(?, ?)

(0, 6)

SECONDS

slide14

Suppose I shoot a bb straight up. It leaves my gun 6 feet above the ground, traveling at 50 feet per second. How much time will it take for the bb to get to its maximum height (nearest hundredth)?

FEET

Sec.

Ft.

(?, ?)

(1, 40)

(0, 6)

SECONDS

slide15

Suppose I shoot a bb straight up. It leaves my gun 6 feet above the ground, traveling at 50 feet per second. How much time will it take for the bb to get to its maximum height (nearest hundredth)?

FEET

Sec.

Ft.

42

(?, ?)

(1, 40)

(0, 6)

SECONDS

slide16

Suppose I shoot a bb straight up. It leaves my gun 6 feet above the ground, traveling at 50 feet per second. How much time will it take for the bb to get to its maximum height (nearest hundredth)?

FEET

Sec.

Ft.

42

(?, ?)

(2, 42)

(1, 40)

(0, 6)

SECONDS

slide17

Suppose I shoot a bb straight up. It leaves my gun 6 feet above the ground, traveling at 50 feet per second. How much time will it take for the bb to get to its maximum height (nearest hundredth)?

FEET

Sec.

Ft.

12

(?, ?)

(2, 42)

(1, 40)

(0, 6)

SECONDS

slide18

Suppose I shoot a bb straight up. It leaves my gun 6 feet above the ground, traveling at 50 feet per second. How much time will it take for the bb to get to its maximum height (nearest hundredth)?

FEET

Sec.

Ft.

12

(?, ?)

(2, 42)

(1, 40)

(0, 6)

(3, 12)

SECONDS

slide19

Suppose I shoot a bb straight up. It leaves my gun 6 feet above the ground, traveling at 50 feet per second. How much time will it take for the bb to get to its maximum height (nearest hundredth)?

FEET

Sec.

Ft.

-50

(?, ?)

(2, 42)

(1, 40)

(0, 6)

(3, 12)

SECONDS

slide20

Suppose I shoot a bb straight up. It leaves my gun 6 feet above the ground, traveling at 50 feet per second. How much time will it take for the bb to get to its maximum height (nearest hundredth)?

FEET

Sec.

Ft.

-50

(?, ?)

(2, 42)

(1, 40)

(0, 6)

(3, 12)

SECONDS

slide21

Suppose I shoot a bb straight up. It leaves my gun 6 feet above the ground, traveling at 50 feet per second. How much time will it take for the bb to get to its maximum height (nearest hundredth)?

FEET

Sec.

Ft.

(?, ?)

(2, 42)

(1, 40)

NEED VERTEX X

(0, 6)

(3, 12)

SECONDS

slide22

Drumroll, plz

FEET

(?, ?)

Vertex:

NEED VERTEX X

SECONDS

slide23

Standard Form

FEET

(?, ?)

Vertex:

seconds

SECONDS

slide24

Standard Form

FEET

(1.56, ?)

Vertex:

seconds

SECONDS

slide25

Standard Form

FEET

(1.56, ?)

Vertex:

seconds

SECONDS

slide26

Standard Form

FEET

(1.56, ?)

Vertex:

seconds

45.0625

feet

SECONDS

slide27

Standard Form

FEET

(1.56, 45.06)

Vertex:

seconds

45.0625

feet

SECONDS

slide29

Standard Form

Vertex:

X coordinate:

Y coordinate: ‘plug in’

slide31

Vertex:

X coordinate:

Y coordinate: ‘plug in’

slide33

X coordinate:

Y coordinate: ‘plug in’

slide35

STOP!

X coordinate:

Y coordinate: ‘plug in’

slide39

How much time to reach the maximum height?

What is the maximum height?

45.06

feet

1.56

seconds

FEET

(1.56, 45.06)

Vertex:

seconds

45.0625

feet

SECONDS

slide41

Asks for HEIGHT Y (feet)

“maximum height?”

Find vertex!

93.77 ft.

slide43

Asks for

TIME X (seconds)

“maximum height?”

Find vertex!

1.63 s.

slide44

Asks for

TIME X (seconds)

“maximum height?”

Find vertex!

slide46

Asks for HEIGHT Y (feet)

“maximum height?”

Find vertex!

546.14 ft.

slide48

Suppose you throw a stone straight up. It leaves your hand 6 feet above the ground, traveling at 50 feet per second. How much time will it take for the stone to get to its maximum height (nearest hundredth)?

Suppose you throw a stone straight up. It leaves your hand 6 feet above the ground, traveling at 50 feet per second. What is the maximum height that the stone will reach (nearest hundredth)?

slide50

Suppose you throw a stone straight up. It leaves your hand 6 feet above the ground, traveling at 50 feet per second. How much time will it take for the stone to get to its maximum height (nearest hundredth)?

Asks for

TIME X (seconds) to get to VERTEX

Suppose you throw a stone straight up. It leaves your hand 6 feet above the ground, traveling at 50 feet per second. What is the maximum height that the stone will reach (nearest hundredth)?

Asks for HEIGHT Y (feet) at VERTEX