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 + 3x

Question 986972: 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.
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
No, it is a quadratic expression. Equations need to equal something. Make it =0 and it is a quadratic equation.
The quadratic formula x= (a/2)* {-b +/- sqrt (b^2-4ac))
It can be derived from the equation Ax^2+Bx+C=0 by subtracting C from both sides and completing the square.
In the equation given, A=1, B=3 C=-23
x=(1/2) (-3 +/- sqrt(9+92)) the -4ac is -4(1)(-23), so that is +92
sqrt 101 is about 10.05
x=(1/2)(-3+/-10.05)
the plus root is
(1/2)7.05 or about 3.53
the minus root is
(1/2)(-13.05)=-6.53

Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.
a) Is = a quadratic equation?

       - No, it is not a quadratic equation.
        It is a quadratic function with a quadratic polynomial in the right hand side.

        It would be a quadratic equation, if it is written in the form = .
        Then you can solve it by using the quadratic formula or factoring.

        The roots of this quadratic equation, = , are x=-3 and x=-4.

        You can factor the quadratic polynomial    in the form = (x+3)*(x+4).

The meaning of this explanation is: use the words and the mathematical terminology correctly!

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