# SOLUTION: y = -x2 - 4x - 3 of this equation what is the line of symmetry? the vertex?

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Question 260712: y = -x2 - 4x - 3 of this equation
what is the line of symmetry?
the vertex?

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vertex (-2,1)
line of symmetry x=-2
 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=4 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: -3, -1. Here's your graph:

Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)

Factor out a negative 1

Now lets concentrate on the quadratic inside the parenthesis and ignore the -1 outside the parenthesis (we'll place it back in later)

In order to factor , first multiply the leading coefficient 1 and the last term 3 to get 3. Now we need to ask ourselves: What two numbers multiply to 3 and add to 4? Lets find out by listing all of the possible factors of 3

Factors:

1,3,

-1,-3, List the negative factors as well. This will allow us to find all possible combinations

These factors pair up to multiply to 3.

1*3=3

(-1)*(-3)=3

note: remember two negative numbers multiplied together make a positive number

Now which of these pairs add to 4? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 4

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 First Number | Second Number | Sum 1 | 3 | 1+3=4 -1 | -3 | -1+(-3)=-4

We can see from the table that 1 and 3 add to 4. So the two numbers that multiply to 3 and add to 4 are: 1 and 3

breaks down to this (just replace with the two numbers that multiply to 3 and add to 4, which are: 1 and 3)

Replace with

Group the first two terms together and the last two terms together like this:

Factor a 1x out of the first group and factor a 3 out of the second group.

Now since we have a common term we can combine the two terms.

Combine like terms.

Remember we factored out a negative 1 to start the problem, so lets reintroduce it back in. So our answer is

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Notice how foils back to . Notice how if we distribute the negative we get: