Graph the quadratic function f(x) = –3.5x².

Graph the quadratic function f(x) = 0.5x² – 1.

Find the axis of symmetry and the vertex of the graph of f(x) = –4x² + 4x – 8.

Graph the quadratic function f(x) = –2x² + 5x – 1.

Graph the quadratic function .

Graph the quadratic function f(x) = (x + 1)(x + 2).

The graph shows the height of a model rocket seconds after it is launched from the ground at 96 feet per second. Where is the height of the rocket increasing? Where is it decreasing?

The function gives the height (in feet) of a ball seconds after it is thrown upward from the roof of a 64-foot tall building. How many seconds after the ball is thrown does it reach its maximum height? What is the ball’s maximum height?

How would you translate the graph of to produce the graph of

Use this description to write the quadratic function in vertex form:
The parent function is vertically stretched by a factor of 2 and translated 14 units right and 6 units up.

Write the function in vertex form, and identify its vertex.

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.

Two identical rubber balls are dropped from different heights. Ball 1 is dropped from a height of 144 feet, and the ball 2 is dropped from a height of 256 feet. Write and graph a function for the height of each ball. Then use the graphs to tell when each ball will reach the ground.

Find the zeros of the function .

The table gives the number of inner tubes, I, sold in a bike shop between 2009 and 2014. Determine which model best fits the data.

Year, t	2009	2010	2011	2012	2013	2014
Inner tubes, I	40	56	74	91	113	127

The graph shows the distance, d, a car is traveling over time, t. What is the average rate of change between points P and Q?

Examine the two graphs of the same four functions. Which function has the greatest function values as x gets larger and larger?

Which function has greater function values as x gets larger and larger? Use a table or graph to identify the function.

A model rocket is launched from a rocket launcher on the ground. The model rocket reaches a maximum height of 31 meters and travels a horizontal distance of 125 meters.

Part A: What type of function should you use to represent the path of the model rocket? Explain.

Part B:  In the context of the given situation, what do the intercepts and maximum point represent?

A student is looking for a quadratic function that fits the points (0, 3), (3, 63), and (–3, –3). He incorrectly believes f(x) = 3x² + x + 3 is the solution, based on his work below. Explain where the student made his first error and what he should have done differently at that point. What is the correct function?

(x, y)	f(x) = ax2 + bx + c
(0, 3)	3 = a(0)2 + b(0) + c
(3, 63)	63 = a(3)2 + b(3) + c
(–3, –3)	–3 = a(–3)2 + b(–3) + c

Because c = 3,
63 = a(3)² + b(3) + 3
–3 = a(–3)² + b(–3) + 3
can be rewritten as
9a + 3b = 60
9a – 3b = –6

This system can be solved by linear combination.

–27a – 9b = –180

–27a + 9b = 18

Substituting one of the ordered pairs gives
63 = 3(3)² + b(3) + 3
63 = 27 + 3b + 3

= b

and the function is f(x) = 3x² + x + 3.