1) You know that the ball was initially a certain height, when it was hit. If you make time(x)=0 (when he began hitting), you can find out the original height of the ball;
y=-16x²+25x+5
y=-16(0)²+25(0)+5
y=5
Therefore, the initial height was 5 meters.
2) Find out the x value of the vertex;
x=-b/2a
x=-25/(2×-16)
x=25/32
x=0.78125 seconds
Substitute this value back into the equation to find the y value of the vertex;
y=-16(0.78125)²+25(0.78125)+5
y=14.765625 meters.
3) Already found above, the time taken (x coordinate of vertex) is 0.78125 seconds.
4) Find the roots when the ball hits the ground; (I used my graphing calculator for this part but you can use the quadratic formula if necessary)
When y=0, x=-0.179 or x=1.742 seconds
1) Bring all terms to the same side;
k²-k-56=0
(k-8)(k-7)=0 <-- factorize equation
k-8=0 OR k-7=0
k=8 or k=7
2) Bring all terms to the same side;
b²+10b+24=0
(b+6)(b+4)=0 <-- factorize
b+6=0 OR b+4=0
b=-6 OR b=-4
Hope I helped :)
