A firework is launched from a platform 75 feet off the ground with an initial velocity of 80 ft/s. The height of the firework can be modeled as a function of time using the equation h =−16x2+80x+75. The firework must go off at 150 feet, to ensure the safety of the onlookers. Between what two time periods must the firework go off? Show your work as it is done in the lesson content and include units of measurement.
(EXAMPLE):
S1 Write the inequality indicating the information in the problem.
−16x2+112x+29 > 200
S2 Put the inequality in standard form.
−16x2 + 112x - 171 > 0
S3 Multiply both sides by -1 and turn the arrow around.
16x2 - 112x + 171 < 0
S4 Factor the inequality.
(4x - 9)(4x - 19) < 0
X = 9/4 or 2.25 or x = 19/4 or 4.75
S5 First interval, x<2.25, select x = 0.
−16(0)2+112(0)+29 > 200
0 + 29 > 200
29 > 200 FALSE. x values in that interval, x < 2.25 are NOT part of the solution.
Second interval, 2.25 < x < 4.75, select x = 3.
−16(3)2+112(3)+29 > 200
-144 + 336 + 29 > 200
221 > 200 TRUE. x values in that interval, 2.25
Third interval, x > 4.75, select x = 5.
−16(5)2+112(5)+29 > 200
-400 + 560 + 29 > 200
189 > 200 FALSE. x values in that interval, x > 4.75 are NOT part of the solution.
Answer: 2.25 ≤ x ≤ 4.75
