A baseball is thrown up in the air from a height of 3 feet with an initial velocity of 23 feet per second. When does the baseball hit the ground?

A) -0.12 seconds
B) 1.44 seconds
C) 1.56 seconds
D) 1.79 seconds

Step-by-step explanation:

This is information that is modeled by a parabolic equation.  The leading coefficient is -16t^2 because we are in feet as opposed to meters (which would be -4.9t^2).  The standard form of this parabolic motion is

where s(t) is the height of the baseball after a certain amount of time has gone by, v0 is the initial vertical velocity, and h0 is the initial height.  Filling in what we have:

We are asked when the ball hits the ground.  If s(t) is our position after a certain time has gone by, and the height of the ball on the ground is no height at all (or 0), then replace s(t) with 0 and factor to solve for t.

Throw that into the quadratic formula or however you like to factor second degree polynomials, and get that the 2 solutions are that

t = -.12 seconds and that t = 1.56 seconds.  We all know that time will NEVER be negative, so the time we want is 1.56 seconds, choice C.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

b