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

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) (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

Start with the given equation.

Take the square root of both sides to "undo" the square.

or Break up the "plus/minus" to form two equations.

or Evaluate the square root of 81 to get 9.

So the solutions are or

# 2 Graphing

Example: Let's solve . If we graph , we get:

Graph of

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

# 3 Factoring

Example: Let's solve

First, we need to factor

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Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .

Now multiply the first coefficient by the last term to get .

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

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

Factors of :
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 .
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 :

First Number	Second Number	Sum
1	8	1+8=9
2	4	2+4=6
-1	-8	-1+(-8)=-9
-2	-4	-2+(-4)=-6

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

So the two numbers and both multiply to and add to

Now replace the middle term with . Remember, and add to . So this shows us that .

Replace the second term with .

Group the terms into two pairs.

Factor out the GCF from the first group.

Factor out 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.

Combine like terms. Or factor out the common term

So factors to .

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Now let's start solving

Start with the given equation.

Factor (see steps above)

or Set each factor equal to zero

or Solve for "x" in each equation

So the solutions are or

# 4 Quadratic Formula

Example: Let's solve

Start with the given equation.

Notice we have a quadratic in the form of where , , and

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

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Subtract from to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the solutions are or
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