Solving Linear and Quadratic Equations and Absolute Value Equations
| Slide 11 |
Example: Find the Equation for a Line
3. Substitute the x and y values for one of the points (2,6) and
solve for b
6 = 2(2) + b
6 = 4+b
6 −4 = b => b = 2
y = 2x + 2
4. Check your answer using the x and y values for the other point
0 = 2(−1) + 2? Yes! |
| Slide 12 |
Example: Find the Equation for a Line
y = 2x + 2
 |
| Slide 13 |
Another Way to Find the Equation for a Line
We have been using the slope- intercept form of the equation for a
line. Another way to find the equation for a line is to use the
point - slope method .
m = slope
 = one point on the line
So, given slope = 2 and point
= (−1, 0):
y − 0 = 2(x − (−1))
y = 2x + 2
Same as before! |
| Slide 14 |
Solving Quadratic Equations
You may need to find the solution to a quadratic equation. To do
this, you must use the distributive , additive , and multiplicative
properties to get the equation into this form:
ax2 + bx + c = 0
Then you can plug a, b, and c into the following equation, which is
called the quadratic formula .
 is called the
discriminant.
|
| Slide 15 |
Solving Quadratic Equations
The solution to a quadratic equation specifies where it crosses the x
axis. A quadratic equation may have 2 solutions:
A quadratic equation may have no solutions:
|
| Slide 16 |
Solving Quadratic Equations
A quadratic equation may have one solution:
 |
| Slide 17 |
Solving Quadratic Equations: Example
So a = 4, b = 12 and c = 6. |
| Slide 18 |
Solving Quadratic Equations: Example
a = 4, b = 12, c = 6
The two solutions are -0.634 and -2.366. |
| Slide 19 |
Solving Quadratic Equations: Example
Check the solutions:
Good! |
| Slide 20 |
Solving Quadratic Equations: Example
We can graph quadratic equations in a manner similar to that for
linear functions :
 |
| Slide 21 |
Graphing Quadratic Equations
 |
| Slide 22 |
Solving Quadratic Equations: Example
Recall the 8 animals who received different doses of a drug and
whose weight gain was measured. The quadratic equation that best
described the relationship between dose and weight gain was:
y = 1.13 − 0.41x + 0.17x2
We can use substitution to find the predicted weight gain, given a
dose. For example, if we know an animal like these received dose 3,
we would predict that the weight gain would be
1.13 − 0.41(3) + 0.17(3)(3) = 1.43 dekagrams.
What if we knew the animal had gained 5 dekagrams, and wanted
to deduce what the dose had been? |
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
December 22nd
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
|
|
|
 |
| |
| "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
| | |
