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Practice Quiz: Unit 5 – Lesson 2
1. Consider the quadratic function f ( x)  x 2  10 x  3 . Complete each task by algebraic reasoning alone. Show all
of your work to support your answers.
a. Rewrite the function rule in vertex form.
b. Does the graph of this function have a maximum or a minimum? Determine the coordinates of the maximum or
minimum point of the graph of this function.
c. What are the coordinates of the x-intercepts of the graph of this function?
d. What is the coordinate of the y-intercept of this function?
2. Solve each quadratic equation.
a. 2 x2  5x  1  0
b. ( x  7)2  10  0
3.
c. 5x  10  2 x2
Find equivalent vertex forms for these functions.

p( x)  x2  6 x  11 ____________________________________

s(n)  n2  n  3 ____________________________________
d. x 2  36  7  10 x
Give examples of quadratic equations with integer coefficients that have:

Two distinct integer solutions___________________________________________________

Two distinct irrational solutions_________________________________________________

Two distinct complex solutions__________________________________________________
4. Using the polynomial f(x) from (1) and g ( x)  3x 2  7 x  4 , find the simplest standard polynomial
expressions for the following combinations of f(x) and g(x). Identify the degree of each result.

f(x) + g(x) ___________________________________________________

f(x) - g(x) ___________________________________________________

f(x) * g(x) __________________________________________________
5. Sketch graphs of these quadratic functions. Explain how the collection of graphs show that quadratic
equations can have: (1) two real number solutions, (2) one repeated real number solution, or (3) no real
number solutions.
a. f ( x)  x 2  6 x  9
b. g ( x)  x 2  6 x  5
c. h( x)  x 2  6 x  14
6. For each function, write the rule in vertex form and find coordinates of the max/min point on its graph
(must do at least 3 by complete the square).
a. f ( x)  x2  10 x  11
b. g ( x)  x 2  4 x  2
c. h( x)  x 2  6 x  15
d.
j ( s )  s 2  2s  6
e. x2  10 x  8  k ( x)
f. x2  14 x  28  m( x)
7.
Use the quadratic formula to solve each of these equations. If the solutions are real numbers, identify
them as rational or irrational numbers. Write non-real complex number solutions in standard form a  bi
a. 2 x2  3x  5  0
b. 2 x2  x  3  0
c. 3x2  x  10
d. 5x  x2  10  0
e. 3x 2  2 x  1  0
f. x 2  x  5  0
g. 4 x( x  5)  29  0
h. 9 x 2  6 x  2  0
8. Consider the equation 2 x 2  9 x  c  0 .
a. Find a value for c so that the equation has two irrational solutions. Explain your reasoning.
b. Find a value for c so that the equation has two rational solutions. Explain your reasoning.
c. Find a value for c so that the equation has two complex number solutions. Explain your reasoning.