Answer: The formula in factored form is h(t) = (t - 5)(t - 11). The true statements are B and D.
Step-by-step explanation: To rewrite the formula in factored form, we need to find two numbers that multiply to 55 and add to -16. These numbers are -5 and -11. So, we can write:
h(t) = t^2 - 16t + 55 h(t) = (t - 5)(t - 11)
This means that the swimmer’s depth is zero when t = 5 or t = 11. These are the times when the swimmer dives into the water and comes back up, respectively. So statement B and D are true.
To find the maximum depth of the swimmer, we need to find the vertex of the parabola. The x-coordinate of the vertex is given by:
x = -b/2a x = -(-16)/2(1) x = 8
The y-coordinate of the vertex is given by:
y = h(8) y = (8 - 5)(8 - 11) y = (-3)(-3) y = 9
So the maximum depth of the swimmer is 9 feet, not 16 feet. Therefore, statement A is false.
Statement C is also false because the swimmer comes back up at t = 11, not t = 16.
Statement E is also false because the function shows that the swimmer dives into the water only once, not twice. The function has only two zeros, which correspond to the times when the swimmer enters and exits the water.
Hope this helps, and have a great day! =)