Name _______________________________________________
Quadratics and Polynomial Functions after School Review
1)
2) Convert to Vertex form and Identify the turning point (vertex)
a) 𝑥 2 + 4𝑥 + 2 = 0
b) −𝑥 2 + 6𝑥 + 4 = 0
c) 4𝑥 2 + 40𝑥 + 3 = 0
3) Solve by using square root property: 10𝑥 2 − 10 = 630
4) Solve by factoring: 2𝑥 2 − 11𝑥 − 21 = 0
5) Solve each equation using the quadratic formula: 6𝑥 2 + 8𝑥 − 25 = −3
6) Solve by completing the square: 3𝑥 2 + 18𝑥 + 5 = 0
7) Write the center-radius form of the circle equation given the following.
A) 𝐶𝑒𝑛𝑡𝑒𝑟: (2, −6)𝑟𝑎𝑑𝑖𝑢𝑠 = 11
B) 𝑐𝑒𝑛𝑡𝑒𝑟 (−7, −3) 𝑟𝑎𝑑𝑖𝑢𝑠 = 3√33
8) Convert 𝑥 2 + 𝑦 2 − 4𝑥 − 6𝑦 + 8 = 0 into center-radius form and identify its center and radius.
9) Find the quadratic equation given the following information.
a) 𝐹𝑜𝑐𝑢𝑠 (−3, 1), 𝐷𝑖𝑟𝑒𝑐𝑡𝑟𝑖𝑥 𝑦 = 5
b) Vertex (3, 1), Focus (3, 5)
c) Vertex (5, -2), Directrix: y = -5
For this one, use the formula: x  h   4 p y  k 
2
10) Find the discriminant and state the number of solutions along with the description of the roots. (real,
imaginary, rational, irrational)
a) −6𝑥 2 − 6 = −7𝑥 − 9
b) 4𝑥 2 + 5𝑥 + 4 = −3𝑥
11) Identify even, odd degree and positive, negative leading coefficient.
12) Is 𝑥 − 5 a factor of 𝑥 3 − 7𝑥 2 + 2𝑥 + 40. Justify your answer.
Use the remainder theorem.
Use long division
Find the other two factors.
13) Divide and state the quotient in quotient-remainder form.
14) Use this graph to answer the following questions.
A) What are the zeroes?
B) What are the factors?
C) Given the point (4, -32) what is the equation in standard form.
D) Put the equation in your calculator. Find the minimum and maximum.
E) Using the factored form of your equation, find the y-intercept.
Verify algebraically whether each function is even, odd, or neither!
1. 𝑓(𝑥) = 𝑥 3 − 6𝑥
2. 𝑔(𝑥) = 𝑥 4 − 2𝑥 2
3. ℎ(𝑥) = 𝑥 2 + 2𝑥 + 1