How do you find and use the vertex?

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# How do you find and use the vertex? - PowerPoint PPT Presentation

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

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

Quadratic function standard form:

### Use Case: Vertical Motion Model

Big question about timeand height?

As seconds increase,

what happens to feet?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Drumroll, plz

FEET

(?, ?)

Vertex:

NEED VERTEX X

SECONDS

Standard Form

FEET

(?, ?)

Vertex:

seconds

SECONDS

Standard Form

FEET

(1.56, ?)

Vertex:

seconds

SECONDS

Standard Form

FEET

(1.56, ?)

Vertex:

seconds

SECONDS

Standard Form

FEET

(1.56, ?)

Vertex:

seconds

45.0625

feet

SECONDS

Standard Form

FEET

(1.56, 45.06)

Vertex:

seconds

45.0625

feet

SECONDS

Standard Form

Vertex:

X coordinate:

Y coordinate: ‘plug in’

Vertex:

X coordinate:

Y coordinate: ‘plug in’

X coordinate:

Y coordinate: ‘plug in’

STOP!

X coordinate:

Y coordinate: ‘plug in’

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

Asks for HEIGHT Y (feet)

“maximum height?”

Find vertex!

93.77 ft.

TIME X (seconds)

“maximum height?”

Find vertex!

1.63 s.

TIME X (seconds)

“maximum height?”

Find vertex!

Asks for HEIGHT Y (feet)

“maximum height?”

Find vertex!

546.14 ft.

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)?

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)?