Your Algebra Homework Can Now Be Easier Than Ever!

Exploring the Vertex Form of the Quadratic Function

Check Your Understanding So Far

The graph of y = x2 is shown at the right. The
following equations are vertical and horizontal
translations of y = x2. Use what you have learned
about translation of the vertex of a quadratic
function to de termine the vertex of the graph of
each equation below. Check your answer using
the Transformation Graphing App.

 

Vertex: ________________________
Vertex: ________________________
Vertex: ________________________
Vertex: ________________________
Vertex: ________________________
Vertex: ________________________

 

What is the most likely equation of the parabola
( quadratic function ) graphed at the right?

Note: The scale is 1.
_________________________________________________

 

 

Studying the Effect of A

1. Return to the Transformation Graphing App
screen, and press until the A= is
highlighted.
 

2. Use the same discovery method you used with B and C to investigate the effect
of A on the graph of the parabola. Be sure to let A be both negative and
positive
.

3. Deactivate the Transformation Graphing App before continuing.

a. Press and select Transfrm.
 
   
b. Select Uninstall.
 

Question for Discussion

1. What effect does changing the value of A have on the graph ? Be sure to discuss
both magnitude and sign change ( positive and negative values).
_________________________________________________________________________

_________________________________________________________________________

Check Your Understanding

Match each equation from items 1–5 with its graph in column 2. Be sure to look at
all the equations and compare them before you answer any questions. Match
equations and graphs first without using your graphing handheld, and then verify
your answers using your graphing handheld.

Note: These examples only investigate changes in the value of A.



Maximum and Minimum Values Come into Focus

When a parabola opens upward, the vertex will
be the lowest point on the curve . Any other
point on the parabola will have a larger value
for y. In the graph shown, the y-value of the
vertex is 1. This is the lowest value of y that is
on the parabola, and it is thus called the
minimum value of the function.
 

The graph shows a parabola with a minimum
value of 1 when x = 2.

Likewise, when a parabola opens down, the
vertex will be the maximum value for y. This
graph shows a function with a maximum value
of -3 when x = -1.



 

Use Your New Skill

Complete the table.

Equation

 
Opens up/
down
 
Function has a
maximum/
minimum
Maximum/
Minimum
value
up minimum 2
     
     
     

A Quick Application

The equation y = -16(x – 4)2 + 259 models the flight of a model rocket where y is the
height of the rocket and x is the time since it was launched. What is the maximum
height of the rocket? How long after it was launched did it reach its maximum?
What does this have to do with this activity?

Student Worksheet

Look at some equations of linear functions and see how translation applies.

1. Use your graphing handheld to graph y = x and y = x + 3 on the same axis. In
what two ways is the second equation a translation of the first?
__________________________________________________________________________
__________________________________________________________________________

Now look at some functions you might not have already studied and see if you can
apply your knowledge in a new situation.

2. The graph of the function y = x3 goes
through the origin (0, 0). Look at the graph
of y = x3 shown and using the point at the
origin as the point you translate (as you did
the vertex), sketch the graph of y = x3 + 2.
Check your answer by graphing y = x3 + 2 on
your graphing handheld.

Note: You can either use 3 for the power of
three
or 3 to select 3:3.


 
   
3. Sketch y = (x – 2)3, and check your answer.
 
   
4. Sketch y = (x + 1)3 – 5, and check your answer.
 
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 April 25th 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 © 2004-2018, Algebra-Answer.Com.  All rights reserved.