Warmup Quick Write 2 minutes Determine some reallife

Warmup: Quick Write (2 minutes) �Determine some real-life events that could be modeled by one of these graphs. What would you label the x-axis, what would you label the y-axis in the events you chose?

Applying Quadratics Objective: find the vertex & roots of a parabola using the calculator and interpret those points in context How are the vertex and roots of a parabola used to solve real-world problems?

Vocabulary �Independent Variable: the factor that represents “x” �Dependent Variable: the factor that represents “y” �Domain: values that can be used for “x” �Function: each input has exactly one output Ex. P(t) : “profit is a function of time”

Height h(t) : height is a function of time Time

Profit P(x) : profit is a function of units sold Number of units sold

Area of rectangle A(w): Area is a function of width (& length) Width of rectangle

Key Points �Vertex: maximum or minimum value ØMax/Min height, area, cost, etc. �Roots (x-intercepts): start & end points ØReach the ground ØBreak even (profit = 0)

Ex) Jumping on a trampoline

The Domain �Values of “x” that can be used in the problem �Can x be a negative number? �Can x be a really large number? �Does x need to be greater than a certain number?

Ex) Diving off a diving board x = time Time is not negative Domain: x ≥ 0

EXAMPLE 1: If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height h after t seconds is given by the equation h(t) = -16 t 2 + 128 t (if air resistance is neglected).

Y = Height (feet) X = time (secs) Domain: x ≥ 0

Y = Height (feet) 3. What was the maximum height of the rocket? (4, 256) Max Height = 256 ft X = time (secs)

Y = Height (feet) 4. How long did it take the rocket to reach its max height? (4, 256) Took 4 seconds X = time (secs)

Y = Height (feet) 5. How long before the rocket hits the ground? (8, 0) X = time (secs) Hit the ground after 8 secs

6. What is the rocket’s height after 7 seconds? t = 7 secs h(t) = 2 -16 t + 128 t h(7) = -16(7)2 + 128(7)

Exit Ticket Take out a sheet of paper (can tear in half and share), WRITE YOUR NAME ON IT, and turn it in before you leave! On a scale of 1 – 10, how well did you learn this lesson today? Do you feel comfortable with quadratic application problems? Why or why not?