How Do I Do?

Question

y = -2x 2(squared) + 11x + 21

How do I work this out manually?
Can I use the quadratic formula?

Answer 1

You insert any value of x, and calculate the corresponding value of y.

Only if you wanted to know the values of x for which y would be zero, and couldn't factorize the resulting equation, would you need to directly use the quadratic formula on the function of x shown on the RHS above.

For the hell of it, rewrite the resulting quadratic equation as :

2 x^2 - 11x - 21 = 0. (I prefer to start with a positive term.)

Fortunately, this readily factorizes, so that you can avoid using the formulaic blunderbus. We end up with:

2 x^2 - 11x - 21 = (2x + 3)(x - 7) = 0, so that

x = - 3/2, OR x = 7.

So the roots for y(x) = 0 are x = - 3/2, OR x = 7.

In general, of course, this means that y = - (2x + 3)(x - 7).

Live long and prosper.

Answer 2

You can, but you don't have to.
-2x² + 11x + 21 = (2x + 3)*(-x + 7)

HTH

Doug