Great video's on this website...should provide you with all the information you would need for showing you know how to solve a system of equation by graphing!
If you need an equation...use this equation editor...download the image and then upload it to your presentation
Launch CodeCogs Equation Editor(click the link to goto the page and then find this link again and launch the editor, save the image...upload it to your presentation!)
y = x
Linear Equation
y = x2
Quadratic Equation
y = x3
Cubic Equation
y = 2x
Exponential Growth
y = (1/2)x
Exponential Decay
y = sqrt(x)
Square Root
y = 1/x
Rational Expressions
y = |x|
Absolute Value
Create a t-chart for every graph and create a image for every graph! Save the images and load them up to your presentation. Make it your own! Put other images (backgrounds, examples, etc) into your presentation as well!
If you need to start over, email me at rthill3@gmail.com and I can share it with you!
Pause the video in the lower left hand corner of the slideshow...Play the video too!!!
Saturday morning....8:00-11:30! I will be at Parkview and will be there to assist on solving the final exam review! Just come...you don't have to let me know you are coming...we will just sit there and work!
If you solve an equation for y, it is in slope intercept form! The number that is in the place of b is the y intercept. The number in the place of m (the coefficient of x) is the slope!
positive slope - the line goes up and to the right (or down and left)
negative slope - the line goes up and to the left (or up and right)
Using Intercepts
To find x and y intercepts...do this
To find the x intercept, make y zero and solve the resulting equation for x
when you get and answer...lets call it a. Then the x intercept is (a, 0)
To find the y intercept, make x zero and solve the resulting equation for y
when you get and answer...lets call it b. Then the y intercept is (0, b)
These two points (a,0) and (0,b) can then be used to graph the line!
Methods for finding slope
Formula
Solve an equation for y (put it in slope intercept form...y = mx + b)
Ax + By = C is standard form....slope is -A/B!
Parallel and Perpendicular lines
Parallel lines...same slope
Perpendicular lines negative reciprocal slope
Finding the zeros
Set the equation up equal to zero and solve...the resulting x value is called the zero.
Usually the equations will be written using function notation
This is the parent graph of a rational expression...just like the others...there is a, h, k
a is positive graph opens up
a is negative graphs open down
h rt/lt (opposite)
k up/dn
You have to know what each of the parent graphs look like....y = x is a linear equation (it makes a line),
y = x^2 is a quadratic equation (it makes a parabola)...use your Parent Graphs presentation to know what it is that causes a graph to change shapes...then understand to change its "style" you change a....
h or k...h is the number inside (x - h) under radical or in denominator (opposite - negative moves it right, positive moves the vertex left) k is the constant....which moves it up or down EXACTLY whatever the number is...
13) Here is an example of a quadratic equation...there is nothing in the (x -h)^2 so h is zero. The constant out there by itself is 5....so that is k. The parabola moves up 5, so the vertex becomes (0,5). Also, because the leading coefficient is 1 it opens up!
14) Square root and k (the constant) is -3 so the pick the graph with the vertex at (0,5)!
15) Multiply 34*630 and add that to (320-34)*267....gross in this problem means the total value of the tickets purchased!
16) This is a difference of two squares (3x + 4)(3x - 4) = 0
Two perfect.....whatever first squared and last term squared
cancel out your middle terms....
6v * 6v = 36v^2.....middle term cancels out....7(-7) = -49
4) Parabola....quadratics equations for parabolas...negative leading
-3 is a....a is negative means the parabola opens DOWN!
5) Combining like terms
Consider the expression below:
5x2 + 7x + 2 - 2x2 + 7 + x2
The terms 5x2, -2x2, and x2 are like terms because they each consist of a constant times x squared.
Now the coefficients of each set of like terms are added. The coefficients of the first set are the constants themselves, 2 and 7. When added the result is 9. The coefficients of the second set of like terms are 5, -2, and 1. Therefore, when added the result is 4.
With the like terms combined, the expression becomes
9 + 7x + 4x2
The Combining Like Terms process is also used to make equations easier to solve.
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