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 986721: 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.
Answer by Alan3354(69443) (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. There's an x^2 term and no other 2nd order terms.
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b) Can it be solved by factoring? If yes, solve it. If not, why not?
Yes, it can.
You factor it, I don't need the practice.
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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?

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:

The online solver ALWAYS says it can be factored. Ignore that.
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d) Use the quadratic formula to solve y = x^2 + 3x - 23 and explain your steps.
See above.
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