SOLUTION: How can you identify the proper way to follow for the equation? out of these ways: 1. Square roots - when x^2 is present, when x^2 and x is present 2. graphing 3. factoring

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: How can you identify the proper way to follow for the equation? out of these ways: 1. Square roots - when x^2 is present, when x^2 and x is present 2. graphing 3. factoring       Log On


   

Question 197703: How can you identify the proper way to follow for the equation?
out of these ways:
1. Square roots - when x^2 is present, when x^2 and x is present
2. graphing
3. factoring
4. quadratic formula
I understand graphing and square roots (somewhat), but when would you use factoring and the quadratic formula? what is the quadratic formula? Can you list the steps of how to do the factoring and quadratic formula? Can you use measures of central tendancy (mean,median,mode) in quadratic functions? Do you have to find the GCF for all of the problems? Would you be able to provide an example problem for when you would factor, and another for when you would use quadratic formula, please?
I am sorry this is so many questions, when you reply can you either do so in complete sentences or with my message above the answers, please?
Thanks, I hope this will help.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Q: Can you use measures of central tendancy (mean,median,mode) in quadratic functions?

A: The mean, median, and mode are totally different concepts compared to the quadratic equation. I don't see you using them in these problems.

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Q: Do you have to find the GCF for all of the problems?

A: You don't have to, but it helps simplify things (sometimes).


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As for the other questions, it's probably best to show you examples...

# 1 Square Root Method:

Example: Let's solve x%5E2=81


x%5E2=81 Start with the given equation.


x=%22%22%2B-sqrt%2881%29 Take the square root of both sides to "undo" the square.


x=sqrt%2881%29 or x=-sqrt%2881%29 Break up the "plus/minus" to form two equations.


x=9 or x=-9 Evaluate the square root of 81 to get 9.



So the solutions are x=9 or x=-9






# 2 Graphing


Example: Let's solve x%5E2%2B5x%2B6=0. If we graph y=x%5E2%2B5x%2B6, we get:




Graph of y=x%5E2%2B5x%2B6


From the graph, we see that the curve intersects with the x-axis at x=-3 and x=-2. So the solutions are x=-3 or x=-2






# 3 Factoring


Example: Let's solve x%5E2%2B6x%2B8=0


First, we need to factor x%5E2%2B6x%2B8


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Looking at the expression x%5E2%2B6x%2B8, we can see that the first coefficient is 1, the second coefficient is 6, and the last term is 8.


Now multiply the first coefficient 1 by the last term 8 to get %281%29%288%29=8.


Now the question is: what two whole numbers multiply to 8 (the previous product) and add to the second coefficient 6?


To find these two numbers, we need to list all of the factors of 8 (the previous product).


Factors of 8:
1,2,4,8
-1,-2,-4,-8


Note: list the negative of each factor. This will allow us to find all possible combinations.


These factors pair up and multiply to 8.
1*8
2*4
(-1)*(-8)
(-2)*(-4)

Now let's add up each pair of factors to see if one pair adds to the middle coefficient 6:


First NumberSecond NumberSum
181+8=9
242+4=6
-1-8-1+(-8)=-9
-2-4-2+(-4)=-6



From the table, we can see that the two numbers 2 and 4 add to 6 (the middle coefficient).


So the two numbers 2 and 4 both multiply to 8 and add to 6


Now replace the middle term 6x with 2x%2B4x. Remember, 2 and 4 add to 6. So this shows us that 2x%2B4x=6x.


x%5E2%2Bhighlight%282x%2B4x%29%2B8 Replace the second term 6x with 2x%2B4x.


%28x%5E2%2B2x%29%2B%284x%2B8%29 Group the terms into two pairs.


x%28x%2B2%29%2B%284x%2B8%29 Factor out the GCF x from the first group.


x%28x%2B2%29%2B4%28x%2B2%29 Factor out 4 from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.


%28x%2B4%29%28x%2B2%29 Combine like terms. Or factor out the common term x%2B2


So x%5E2%2B6x%2B8 factors to %28x%2B4%29%28x%2B2%29.


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Now let's start solving x%5E2%2B6x%2B8=0


x%5E2%2B6x%2B8=0 Start with the given equation.


%28x%2B4%29%28x%2B2%29=0 Factor (see steps above)


x%2B4=0 or x%2B2=0 Set each factor equal to zero


x=-4 or x=-2 Solve for "x" in each equation


So the solutions are x=-4 or x=-2






# 4 Quadratic Formula


Example: Let's solve x%5E2-22x%2B117=0



x%5E2-22x%2B117=0 Start with the given equation.


Notice we have a quadratic in the form of Ax%5E2%2BBx%2BC where A=1, B=-22, and C=117


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%28-22%29+%2B-+sqrt%28+%28-22%29%5E2-4%281%29%28117%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-22, and C=117


x+=+%2822+%2B-+sqrt%28+%28-22%29%5E2-4%281%29%28117%29+%29%29%2F%282%281%29%29 Negate -22 to get 22.


x+=+%2822+%2B-+sqrt%28+484-4%281%29%28117%29+%29%29%2F%282%281%29%29 Square -22 to get 484.


x+=+%2822+%2B-+sqrt%28+484-468+%29%29%2F%282%281%29%29 Multiply 4%281%29%28117%29 to get 468


x+=+%2822+%2B-+sqrt%28+16+%29%29%2F%282%281%29%29 Subtract 468 from 484 to get 16


x+=+%2822+%2B-+sqrt%28+16+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%2822+%2B-+4%29%2F%282%29 Take the square root of 16 to get 4.


x+=+%2822+%2B+4%29%2F%282%29 or x+=+%2822+-+4%29%2F%282%29 Break up the expression.


x+=+%2826%29%2F%282%29 or x+=++%2818%29%2F%282%29 Combine like terms.


x+=+13 or x+=+9 Simplify.


So the solutions are x+=+13 or x+=+9