Question

5.An owl swoops down from its perch in a tree at 30 feet to catch field mice. It follows the function h=6t2 −24t+30
, where t is the time in seconds and h is the height in feet. Which of the following best interprets the vertex?(1 point)
Responses

(30,0)
left parenthesis 30 comma 0 right parenthesis

(2,6)
left parenthesis 2 comma 6 right parenthesis

(6,2)
left parenthesis 6 comma 2 right parenthesis

(0,30)
4.Luca is building a garden in his backyard. He needs to erect a fence to keep his dog Luna from digging in it. He has enough materials for a fence with 120 feet around the perimeter. This function is represented by the formula A=−w2+60w
, where A
is the area and w is the width. Which of the following correctly identifies the x-intercept(s)?(1 point)
Responses

(60,0)
and (30,900)
left parenthesis 60 comma 0 right parenthesis and left parenthesis 30 comma 900 right parenthesis

(60,0)
left parenthesis 60 comma 0 right parenthesis

(0,0)
and (60,0)
left parenthesis 0 comma 0 right parenthesis and left parenthesis 60 comma 0 right parenthesis

(0,0)
3.Question
A high diver jumps off a platform 40 feet above the water. The height, h, in feet of the diver above the water at any time, t, in seconds is given by the function h=−16t2+32t+40
. Plot points to graph the equation. Which ordered pair represents the vertex?(1 point)
Responses

(1, 56)
open paren 1 comma space 56 close paren

(56, 1)
open paren 56 comma space 1 close paren

(2.9, 0)
open paren 2 point 9 comma space 0 close paren

(0, 40)
open paren 0 comma space 40 close paren
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2.While hiking, Marek throws a rock off a cliff that is roughly 10 meters above a lake. This situation is modeled by the equation h=−4.9t2+10
, with h representing the height in meters and t the time in seconds. If you were to set up a table to determine when the rock hits the water, what would be a reasonable scale for the range?(1 point)
Responses

110
1 tenth

5
5

10
10

2
2
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1.A volleyball is served by a 6-foot player at an initial upward velocity of 33 feet per second. The situation is modeled by the equation h=−16t2+33t+6
h representing the height in feet and t representing the time in seconds. Using this equation, define the domain of the ball when it reaches its maximum height.(1 point)
Responses

23.01 feet
23.01 feet

−1.03 seconds
negative 1.03 seconds

1.03 seconds
1.03 seconds

1.22 seconds

Answer 1

Here are the correct choices with brief justification:

5. Owl: (2, 6) — vertex at t = -b/(2a) = 24/12 = 2, h = 6(4) −24(2) +30 = 6.

4. Fence: (0,0) and (60,0) — solve −w^2 + 60w = 0 ⇒ w(−w + 60) = 0.

3. Diver: (1, 56) — vertex at t = −32/(2·−16) = 1, h = −16(1)^2 + 32(1) + 40 = 56.

2. Rock off cliff: 2 — reasonable vertical scale for height from 10 m down to 0 m is 2 (1 or 2 are sensible; 2 is best among the choices).

1. Volleyball: 1.03 seconds — time of maximum height t = −33/(2·−16) ≈ 1.03 s.