Question

Help please. A math lib question about quadratic equations

Answer 1

Answer:

A

Step-by-step explanation:

A.

at 1.5 seconds

h=-16(1.5)²+30(1.5)+6

=-16×2.25+45+6

=-36+45+6

=15 ft

which is correct.

B.

h=-16(t²-30/16 t)+6

=-16(t²-30/16t+(15/16)²-(15/16)²)+6

=-16(t-15/16)²-16(-225/256)+6

=-16(t-15/16)²+225/16 +6

=-16(t-15/16)²+(225+96)/16

=-16(t-15/16)²+321/16

it is at maximum height when t=15/16 seconds

so B is not true.

C.

when t=15/16 seconds

h=321/16 ft=20 1/16 ft

height of fence=20 ft

so it will clear the fence.

C is not true.

D.

when h=0

-16t²+30t+6=0

8t²-15t-3=0

$t=\frac{15\pm\sqrt{225-4 \times 8 \times (-3)} }{2 \times 8} \\=\frac{15 \pm \sqrt{225+96} }{16} \\=\frac{15\pm \sqrt{321} }{16} \\rejecting~negative~sign\\t=\frac{15+\sqrt{321}}{16} \approx. 2.057 seconds$

it hits the ground in 2.057 seconds

so D is not true.