Homework due Weds May 12th
pg 499 #1-16 ALL, #17-25 ODD
pg 556 #43-53 ALL
WHAT FUN?!?!?
Graphing
Square Rooting
Factoring
Completing the Square
Quadratic Formula
Graphing Calculator
OH MY!!
You should be knowledgeable in all of these techniques and be able to evaluate a quadratic equation or function and determine the best method to use to obtain a solution. Are YOU an ALGEBRA-TICIAN??
This unit is dedicated to Charles, our honorary Algebra-tician!
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I cannot complete the square. ever. i always mess up!!!!
ReplyDeleteyou could use the quadratic formula instead
ReplyDeleteJust wondering, when it says slove for x, do they mean the roots or the axis of symmetry?
ReplyDeletea very good question indeed... I want you to think back to your "roots" of beginning in Algebra. When solving an equation such as:
ReplyDelete3x + 4 = 25
... you are attempting to isolate the variable 'x' so that you can determine which value or values, when substituted for 'x' will make the equation true. In the linear equation above, the lone solution is x = 7... ca-peeesh?
When you are asked to solve an equation such as:
Case I
x^2 - 5x + 6 = 0
... the goal is the same, to find the value or values for 'x' that will make the equation true (hopefully, this answered your question already... if not, read on). We have learned that one way to solve a quadratic trinomial equation is to set it equal to zero and attempt to factor. In this case, factoring yields:
(x-2)(x-3)=0
... which values of 'x' make this equation true? Well, with help from the (duh!) ZERO PRODUCT PROPERTY, we quickly see that x=2,3 are the solutions. We have also learned that if factoring doesn't work, we can always Complete the Square or use the Quadratic Formula.
The previous problem is similar, but not the same as the problem which says solve & graph the quadratic equation:
CASE II
y = x^2 - 5x + 6
In this case, you will find an axis of symmetry of x = 2.5, and roots (aka, zeroes, solutions, x-intercepts) of 2 & 3. Of course, with the 'y=' comes a graph in the coordinate plane.
I know this was a longer answer than you would have liked, but this is crucial to your understanding. If we are solving an equation in one variable (Case I) we just need to find the values of 'x' that make the equation true. If we are graphing an equation in two variables (such as Case II), there is add'l work to do... the axis of symmetry is not a 'solution' it is simply a line of reflection that helps us find the vertex and graph the symmetrical parabola. The roots/zeroes/x-intercepts are considered the solution(s).
E-Z- Schmeezy, huh?!