Michael P. answered • 06/29/14

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A possibly better solution to this problem, given that it may not always be multiple choice, is to actually find the zeroes of this function.

First you would let f(x)=-8x^2+4x+7=0

Now, since you were asked for an approximate answer, and this is a quadratic equation, you can use the quadratic formula, which says that the roots (the zeroes) of a function of this type (ax^2+bx+c=0) are equal to:

x=(-b+sqrt(b^2-4ac))/2a

and

x=(-b-sqrt(b^2-4ac))/2a

Plugging in a=-8, b=4 and c=7 simplifies to

x=(1+sqrt(15))/4

and

x=(1-sqrt(15))/4

Plugging these into our calculators gives the last solution set.

You may also be familiar with factoring quadratic equations into the form (x-n)(x-m)=0 in order to solve them. With this one, a hint that you should use the quadratic equation is that the constant term (c or 7 in this problem) is prime, that is there are no integers that you can multiply together to get seven