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John is hitting baseballs. The height of the ball is given by y=-16x^2+25x+5 (x is seconds, y is height in feet)

1.) What is the original height of the ball hitting the bat?

2.) What is the maximum height that the ball reaches?

3.) How long does it take for the ball to reach its maximum height?

4.) When does the ball hit the ground?

Find the Vertex of the Parabola.

1.) k^2-56=k

2.) b^2+10b=-24

Respuesta :

kritter1
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 :) 

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