Do Now: A parabola has an axis of symmetry y = 3 and passes through (2,1). Find another point that lies on the graph Identify the focus, directrix, and axis of symmetry of x = 2y2

Do Now: A parabola has an axis of symmetry x = 3 and passes through (2,1). Find another point that lies on the graph

Review Chapter 2

Write a rule for g  

Write an Equation Points: (-1,0), (5,3), (7,0) Passes through (1,12) and has a vertex (10,-4)

Graph: y = 3x2 – 6x + 4

Graph: y = -(x +3)2 + 5

Graph: y = 2(x+3)(x-1)

Write an Equation Vertex: (10,-4); passes through (1,12) Points: (-1,0), (5,3), (7,0) Passes through (4,3); x-intercepts of -1 and 5

Calculator Explain why a quadratic function models the data. Then find the model. 1) 2) x 2 4 6 8 10 f(x) -13 -34 -63 -100 Year, t 1 2 3 4 5 Price, p $603.46 $695.39 $871.96 $972.35 $1224.53 $1571.52

An object is launched directly overhead at 36 meters per second An object is launched directly overhead at 36 meters per second. The height (in meters) of the object is given by h(t) = -16t2 + 36t + 5where t is the time (in seconds) since the object was launched. How long is it in the air? How high does it get? When is it at its highest? For how many seconds is the object at or above a height of 25 meters?

Write an Equation Vertex: (-3,2) Focus: (-3,-5) Points: (-1,0), (5,3), (7,0) Directrix: x = -2 vertex: (2,0)

Example 2 A meteorologist creates a parabola to predict the temperature tomorrow, where x is the number of hours after midnight and y is the temperature (in degrees Celsius). a. Write a function f that models the temperature over time. What is the coldest temperature? b. What is the average rate of change in temperature over the interval in which the temperature is decreasing? increasing? Compare the average rates of change.

Word Problem An electricity-generating dish uses a parabolic reflector to concentrate sunlight onto a high-frequency engine located at the focus of the reflector. The sunlight heats helium to 650°C to power the engine. Write an equation that represents the cross section of the dish shown with its vertex at (0, 0). What is the depth of the dish?