SOLUTION: Three parts and uses the quadratic equation: x^2 - 18x + 72 = 0 Part a. 1. Graph the quadratic equation and: a. Label and include the ordered pair for the vertex on the grap

Question 900370: Three parts and uses the quadratic equation: x^2 - 18x + 72 = 0
Part a.
1. Graph the quadratic equation and:
a. Label and include the ordered pair for the vertex on the graph.
b. Label and include the ordered pair(s) for the x--intercepts on the graph.
c. How are the solutions identified from the graph?
Part b.
1. Solve the quadratic equation by using the "completing the square" method.
2. What do you notice about the answer you found here and where the x-intercepts of the graph are in part a?
Part c.
1. Solve the quadratic equation by using the quadratic formula. Show all your work.
2. Compare your answer to what you found in part a and b. What do you notice about the answers?

Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!

Solved by pluggable solver: COMPLETING THE SQUARE solver for quadratics

Read this lesson on completing the square by prince_abubu, if you do not know how to complete the square.
Let's convert to standard form by dividing both sides by 1:
We have: . What we want to do now is to change this equation to a complete square . How can we find out values of somenumber and othernumber that would make it work?
Look at : . Since the coefficient in our equation that goes in front of x is -18, we know that -18=2*somenumber, or . So, we know that our equation can be rewritten as , and we do not yet know the other number.
We are almost there. Finding the other number is simply a matter of not making too many mistakes. We need to find 'other number' such that is equivalent to our original equation .

The highlighted red part must be equal to 72 (highlighted green part).

, or .
So, the equation converts to , or .

Our equation converted to a square , equated to a number (9).

Since the right part 9 is greater than zero, there are two solutions:

, or

Answer: x=12, 6.

Solved by pluggable solver: Quadratic Formula

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

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=1, b=-18, and c=72

Negate -18 to get 18

Square -18 to get 324 (note: remember when you square -18, you must square the negative as well. This is because .)

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator

Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator

Divide

So another answer is

So our solutions are:

or

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