Midterm Page 3

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...

Midterm Page 2 (9-17)

9)  Combining Like Terms

10-12) FOIL

First, Outside, Inside, Last

• 2x*3x = 6x^2
• 2x + 3x= 5x

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

Page 1 of Midterm (1-8)

1)  h and k are the vertex...

• h is number underneath the radical (opposite)
• k is the y coordinate of the vertex


• domain (input) - x values
• range (output) - y values

2)  (a + b)² = a² +2ab + b²

3)  (a + b)(a - b) = Difference of two squares...

• 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.