Quadratic Equations and Functions Review

8.1 The Square Root Property and Completing the Square
Review: The Square Root Property ; solving quadratic equations by using the square root
property; solving quadratic equations by completing the square.

8.2 The Quadratic Formula
Review: Solving quadratic equations using the quadratic formula; the discriminant

8.3 Quadratic Functions and Their Graphs
Graphs of quadratic functions (parabolas opening upward or downward; vertex; axis of
symmetry); graphing quadratic functions with equations in the form

; finding intercepts; graphing and finding the vertex of quadratic
functions whose equation is in the form ; applications of quadratic
functions; minimum or maximum values of quadratic functions.

8.4 Equations Quadratic in Form
Solving equations that are quadratic in form – identify an appropriate u-substitution that
transforms the original equation into one that is quadratic; solve the u-equation; replace
the u variable with the equivalent x variable expression; solve to obtain the final answer
in terms of the x variable .

8.5 Quadratic and Rational Inequalities
Solving quadratic inequalities: Approach 1 – Find the x-intercepts of the corresponding
quadratic function and then determine the intervals that correspond to solutions ; then use
test values from each interval to determine the signs of the quadratic expression on the
intervals ; Approach 2 – use the graph of the corresponding quadratic function; find the x-
intercepts and then solve the inequality by sketching the graph.

Solving rational inequalities – find all x-values that make the numerator and denominator
zero ; use these values to partition the real number line into intervals ; use a test value from
each interval to determine the sign of the rational expression on each interval.

10.1 Distance and Midpoint Formulas; Circles
The Distance Formula and the Midpoint Formula; definition of a circle; standard form of
the equation of a circle ; finding the standard form of a circle’s equation given the circle’s
center and radius; finding the center and radius of a circle; finding the standard form of a
circle’s equation by completing the square; graphing circles.

Review Problems
Chapter 8
p. 634, Review Problems: 1-54
p. 636, Chapter 8 Test: 1-25
Chapter 10
p. 788, Review Problems: 1-10
p. 790, Chapter 10 Test: 1-5