, what is the vertex

Question

The height of a ball in feet is modeled by f(x)= -16^2+80x

 

Answer 1

Hello, Lindsey,

 

I suppose that you mean the following equation:  f(x)=y= -16x² + 80x.  Here are some quick steps to follow.  By the way this problem can also be entered into the graphing mode of the graphing calculator.  Then you could check the table (F5) for the parabola's maximum height (vertex).  However, here is how to do it by hand:

Note:  y= height of ball in feet

1)  y= -16x² + 80x+0                                     2)  Remember the Standard Form:  y=ax² +bx +c

 

3.  a= -16,   b=80,   c=0       

 

4)  Quick method:  Use this formula to find the maximum "x" value:  x_max= - (b)/2a   .

 

 

5)  Now, use substitution for the values of "b" and "a":

 

                                         x= -(80)    =   -80   =  -5  = 5= 2.5   maximum "x" value

                                              2(-16)        -32       -2     2

 

6) You will need the maximum "y" value, too, in order to have a maximum vertex point (x,y).  All you need to do now is to substitute the "x" value into your equation in order to find the maximum height value, which will be your "y" value.

 

y= -16 (5/2)²+ 80 (5/2)

 

I am going to let you finish you problem.  I hope that I have helped.   Susan C.