# 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.

8.3 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.

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 .

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

 Prev Next

Start solving your Algebra Problems in next 5 minutes!

2Checkout.com is an authorized reseller
of goods provided by Sofmath

Attention: We are currently running a special promotional offer for Algebra-Answer.com visitors -- if you order Algebra Helper by midnight of September 17th you will pay only \$39.99 instead of our regular price of \$74.99 -- this is \$35 in savings ! In order to take advantage of this offer, you need to order by clicking on one of the buttons on the left, not through our regular order page.

If you order now you will also receive 30 minute live session from tutor.com for a 1\$!

You Will Learn Algebra Better - Guaranteed!

Just take a look how incredibly simple Algebra Helper is:

Step 1 : Enter your homework problem in an easy WYSIWYG (What you see is what you get) algebra editor:

Step 2 : Let Algebra Helper solve it:

Step 3 : Ask for an explanation for the steps you don't understand:

Algebra Helper can solve problems in all the following areas:

• simplification of algebraic expressions (operations with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots (radicals), absolute values)
• factoring and expanding expressions
• finding LCM and GCF
• (simplifying, rationalizing complex denominators...)
• solving linear, quadratic and many other equations and inequalities (including basic logarithmic and exponential equations)
• solving a system of two and three linear equations (including Cramer's rule)
• graphing curves (lines, parabolas, hyperbolas, circles, ellipses, equation and inequality solutions)
• graphing general functions
• operations with functions (composition, inverse, range, domain...)
• simplifying logarithms
• basic geometry and trigonometry (similarity, calculating trig functions, right triangle...)
• arithmetic and other pre-algebra topics (ratios, proportions, measurements...)

ORDER NOW!