Compare the graph of with the graph of .

Mary incorrectly graphed the function using transformations of the graph of . First she stated what transformations to perform, and then she drew the graph. Describe any errors.

Use this description to write the quadratic function:
The parent function is vertically stretched by a factor of 2 and translated 7 units right and then translated 5 units up.

If , which of the following is equal to ?

Use symmetry to graph the quadratic function f(x) = 3x² + 3x – 2.

Graph the quadratic function f(x) = (x – 4)(x + 1).

Find the maximum value of each quadratic function. Then decide which function has the greater maximum value.

--Quadratic Function 1: The function whose equation is .
--Quadratic Function 2: The function whose graph is shown.

A rocket leaves a launcher at a height of 6 feet off the ground with an initial velocity of 128 feet per second. The equation describing the rocket's height after t seconds is Find the maximum height reached by the rocket and how many seconds it takes for the rocket to reach that height.

Write an equation in standard form for a parabola with vertex and directrix .

Write an equation in standard form for a parabola with focus and directrix .

A parabola has focus (1.5, 0) and directrix x = 1.5.

Part A: What is the equation of the parabola?

Part B: Without graphing, tell the direction in which the parabola opens. How do you know?

The figure shows the graph of the quadratic function . Find the average rate of change between points F and G and between points G and H. Write down the greater rate of change.

Make a scatter plot of the data. Then find an equation of the quadratic function that models the data.

x	0	1	2	3	4	5	6	7	8
y	4	8	14	22	32	44	58	74	92

A  satellite television receiver is a parabolic dish with an equation of  . The receptor is placed at the focus. How far from the vertex of the parabola is the receptor? Explain your reasoning.

A spotlight uses a parabolic reflector, a surface with a parabolic cross section, and a light bulb at the focus of the parabola. If the bulb is 3.5 inches from the vertex of the reflector, what is the equation of the parabola? Explain your reasoning.

An observatory has a large antenna to collect signals from space. The antenna has a curved surface with a parabolic cross section, and a microphone is located at the focus of the parabola. The microphone is 16 feet from the vertex of the parabola. Write an equation that can be used to model the parabola. Explain how you found your equation.

Consider the graph of . Find the intercepts. Find the vertex and state whether it is a minimum or a maximum. Determine the intervals where is increasing and decreasing and the intervals where it is positive and negative.

The table below gives the stopping distance y (in 100 meters) for a train traveling on a track at various speeds x (miles per hour).

Speed, x (mi/h)	60	65	70	75	80	85	90	95	100
Distance, y (100 m)	35	50	70	95	125	160	200	245	295

Find an equation of the quadratic function that models the data, and predict the stopping distance for the train traveling at 105 miles per hour.

Todd graphs a quadratic function. The graph of his quadratic function passes through the points
, and . Which quadratic function could be Todd’s function?

The function f is a quadratic function whose graph opens downward and has its vertex at (–3, 4). The x-intercepts of f are –5 and –1.
The function g is also a quadratic function and is shown in the table below.

x	g(x)
–3	3
–2	0
–1	–1
0	0
1	3
2	8
3	15

Part A: For each function, find the axis of symmetry of its graph. Explain how you found the axes of symmetry and compare their locations in the coordinate plane.
Part B: Function f is represented by a verbal description. Function g is represented numerically in a table. Are those the best representations for comparing the locations of the axes of symmetry? If so, explain why. If not, how would you represent f and g to make their axes of symmetry easier to compare?