<span>The discriminant of a quadratic equation is the b^2-4ac portion that the square root is taken of. If the discriminant is negative, then the function has 2 imaginary roots, if the discriminant is equal to 0, then the function has only 1 real root, and finally, if the discriminant is greater than 0, the function has 2 real roots. So let's look at the equations and see which have a positive discriminant.
f(x) = x^2 + 6x + 8
6^2 - 4*1*8
36 - 32 = 4
Positive, so f(x) has 2 real roots.
g(x) = x^2 + 4x + 8
4^2 - 4*1*8
16 - 32 = -16
Negative, so g(x) does not have any real roots
h(x) = x^2 – 12x + 32
-12^2 - 4*1*32
144 - 128 = 16
Positive, so h(x) has 2 real roots.
k(x) = x^2 + 4x – 1
4^2 - 4*1*(-1)
16 - (-4) = 20
Positive, so k(x) has 2 real roots.
p(x) = 5x^2 + 5x + 4
5^2 - 4*5*4
25 - 80 = -55
Negative, so p(x) does not have any real roots
t(x) = x^2 – 2x – 15
-2^2 - 4*1*(-15)
4 - (-60) = 64
Positive, so t(x) has 2 real roots.</span>
To solve this we are going to use the free distance fallen formula: where is the distance is the gravity of Earth is the time in seconds
We know from our problem that the penny fell off the top of the building and hit the sidewalk below 3.1 seconds later, so . Lets replace the value in our formula: meters
We can conclude that the penny fell a distance of 47.098 meters
is the distance
is the gravity of Earth 
is the time in seconds
. Lets replace the value in our formula:
meters