SOLUTION: a) Is y = x^2 + 7x + 12 a quadratic equation*? Why or why not? b) Can it be solved by factoring? If yes, solve it. If not, why not? c) As it happens, the equation y = x^2 + 3

Question 987008: a) Is y = x^2 + 7x + 12 a quadratic equation*? Why or why not?
b) Can it be solved by factoring? If yes, solve it. If not, why not?
c) As it happens, the equation y = x^2 + 3x - 23 also cannot be solved by factoring. One method of solving quadratic equations, however, that will solve ALL of them, is called using the quadratic formula. Can you state and explain the quadratic formula?
d) Use the quadratic formula to solve y = x^2 + 3x - 23 and explain your steps.
I really need help with this one!!!!! Thanks
Found 2 solutions by josgarithmetic, macston:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Can you decompose the polynomial into something of a form (x+r)(x+s) ? If not, then this method of the lesson will always work:
http://www.algebra.com/my/Completing-the-Square-to-Solve-General-Quadratic-Equation.lesson?content_action=show_dev
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
.
a) Is y = x^2 + 7x + 12 a quadratic equation*? Why or why not?
Yes it is. A quadratic equation is an equation of degree 2
(the variable to highest power is raised ^2).
.
b)

.
d)
.

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=101 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 3.52493781056044, -6.52493781056044. Here's your graph:

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