Download Name: Date: Graphing Quadratics: Standard and Vertex form

Name:___________________________________________
Date:______________________
Graphing Quadratics: Standard and Vertex form
Algebra
1. Identify each type of function.
a. 𝑓(𝑥) = 𝑥 3 − 3𝑥
b. 𝑔(𝑥) = 2|𝑥 + 4| − 3
c. ℎ(𝑡) = 3(2)𝑡
2. Rewrite each quadratic function in standard form and state the value of the leading coefficient.
a. 𝑦 = 3 − 𝑥 2 + 𝑥
b. 2𝑥 + 3𝑥 2 = 𝑦
c. 𝑦 = 5𝑥 − 10 − 4𝑥 2
3. Use the given table to state the turning point of the function and whether it opens upwards or downwards.
𝑥 3 4 5 6 7 8
9
𝑦 −2 1 4 1 −2 −7 −14
𝑥 −1 0 1 2 3 4 5
𝑦 3 8 11 12 11 8 3
𝑥 −5 −4 −3 −2 −1 0 1
𝑦 10 3 −2 −5 −6 −5 −2
4. Graph the function 𝑓(𝑥) = 𝑥 2 + 4𝑥 − 5 on the graph provided and answer the following questions.
a. State the coordinates of the turning point. Is the
point a maximum or a minimum?
b. State the range of the function.
c. Over what interval is the function decreasing?
d. What are the zeros of the function?
e. On what interval is the function negative?
5. For the quadratic 𝑦 = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 fill in the blanks.
The parabola will open upwards if ___________________ and will have a _______________𝑦 −value.
The parabola will open downwards if ___________________ and will have a _______________𝑦 −value.
6. The parabola created by 𝑓(𝑥) = 𝑥 2 + 6𝑥 + 7 has a axis of symmetry of 𝑥 = −3. Determine the range of the
function.
7. The height of an object traveling through the air can be represented by the function ℎ(𝑡) = −16𝑡 2 + 64𝑡 + 60.
a. What is the maximum height in feet?
b. At what time does the object hit the ground?
c. Over what interval is the height decreasing?
d. After how many seconds does the object
reach its maximum height?
e. What is the range of the function?
8. For each function state the turning point and whether the function opens upwards or downwards.
a. 𝑓(𝑥) = (𝑥 − 2)2 + 4
b. 𝑔(𝑥) = −2(𝑥)2 − 6
c. ℎ(𝑥) = −(𝑥 + 3)2
9. Graph the function 𝑓(𝑥) = (𝑥 − 2)2 − 4 and answer the following questions.
a. What is the turning point of the function
b. Over what interval is the function increasing?
c. What are the zeros of the functions?
d. On what interval is the function negative?
10. For each function state the turning point, concavity, graph and label each graph with the letter.
a. 𝑓(𝑥) = (𝑥 − 1)2 − 4
b. 𝑔(𝑥) = −(𝑥 + 4)2 + 9
c. ℎ(𝑥) = 2(𝑥)2 − 8
d. 𝑗(𝑥) = −3(𝑥 + 1)2 + 10
11. The cost per iPhone produced at the factory depends upon on how many phones are produced per day. The
1
cost function is modeled by 𝐶(𝑛) = 100 𝑛2 − 2𝑛 + 500, where 𝑛 is the number of phones produced in a day and
𝐶(𝑛) is the unit cost in dollars per phone.
a. Calculate 𝐶(75), and give an interpretation of
your answer in terms of the scenario
described.
b. Does the cost have a minimum or maximum
value? Find your calculator to find the value.
c. Does this function have and real zeros? Why or why not?