Your Algebra Homework Can Now Be Easier Than Ever!

Midterm Exam Number Two Review

• Be able to find a linear formula from a verbal description. Look for words like “...is a
linear function of...”, “...has a straight line graph...”, “items sell for $0.15 each” (tells
you TR is linear), “it costs you $10 to make each item” (tells you TC is linear).

• Given a formula for distance , you should be able to find formulas for average trip
speed and average speed over an interval of a specified length (see WS 12). You
should be able to do this in other contexts as well.

e.g., Given the total amount of water in a vat, W(t), find formulas for overall and
incremental rates of change . Or, given the TC, find formulas for AC and MC.

• Given a formula for price per item as a function of q, you should be able to find
formulas for TR(q) and MR(q):

TR(q) = p · q

MR(q) = TR(q + 1)− TR(q)

(see WS 13)

• If you have formulas for MR and MC and you want the quantity that maximizes
profit, you should be able to set MR = MC and solve for q . Round up to the nearest
whole number of items (being careful if q is measured in hundreds, e.g., q = 2.13 is
a whole number of items .) If you get two positive quantities at which MR = MC,
remember profit is maximized at a transition from MR > MC to MR < MC.

• You should know when and how to apply the vertex formula /method. Suppose f(x) =
ax2 + bx + c with a < 0. Then the vertex formula gives the value of x that
maximizes
f(x). To find the maximum value of f(x), you can plug   back into
f(x).

Typical questions:

– Find the time/quantity at which (some quadratic function ) is largest/smallest/
lowest /highest/maximized/minimized.

– Find the largest/smallest/ lowest /highest/maximum/minimum value of (some
quadratic function).

Special note: If profit is a quadratic function and you use the vertex formula to
maximize profit and is not a whole number, then you should round to the
nearest whole number quantity.

• The vertex formula can also give information about when a quadratic function is
increasing/decreasing. In particular, if you’re asked to find an interval on which a
function is increasing, draw a rough sketch.

e.g.:
f(x) = −3x2 + 12x − 19 opens down, vertex at

so f(x) increases from x = 0 to x = 2, for instance

As opposed to g(x) = −3x + 4 which is always decreasing.

• Know when and how to apply the quadratic formula. Use the quadratic formula to
solve an equation of the form ax2 + bx + c = 0.

Example: Suppose profit is given by

P(q) = −3q2 + 12q − 19.

P(q) is a quadratic function but it is not a quadratic equation. However if we want to
know what quantity makes a profit of $15, then we can solve the quadratic equation

−3q2 + 12q − 19 = 15

by rewriting it as

−3q2 + 12q − 34 = 0

and applying the quadratic formula.

• You should understand how TR, TC and profit can be read as areas of rectangles
under the price and AC per item functions. (WS 15)

• You should be able to answer questions about TR, TC, and profit given the formulas
for p and AC. (WS 15)

• You should have a clear understanding of how all of the following are related:

– TR and MR and AR and p
– TR(q) = p · q, MR(q) = TR(q + 1) − TR(q),

– TC, FC, VC, AC, AVC, MC:

• You should understand that breakeven price is

– the smallest value of AC (so if AC is a quadratic function of q this is the “y”-
coordinate of the vertex of AC)

– the “y”-coordinate of the point where AC and MC intersect

• You should be able to determine distance travelled from informatino about speed. In
particular, if speed is a known linear function of time, then you should be able to
describe distance as a quadratic function of time, and answer questions about those
functions. (WS 17)

Prev Next

Start solving your Algebra Problems in next 5 minutes!

Algebra Helper
Download (and optional CD)

Only $39.99

Click to Buy Now:


OR

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 March 29th 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!

Algebra Helper
Download (and optional CD)

Only $39.99

Click to Buy Now:


OR

2Checkout.com is an authorized reseller
of goods provided by Sofmath
Check out our demo!
 
"It really helped me with my homework.  I was stuck on some problems and your software walked me step by step through the process..."
C. Sievert, KY
 
 
Sofmath
19179 Blanco #105-234
San Antonio, TX 78258
Phone: (512) 788-5675
Fax: (512) 519-1805
 

Home   : :   Features   : :   Demo   : :   FAQ   : :   Order

Copyright © 2004-2024, Algebra-Answer.Com.  All rights reserved.