(08.02 MC)The function f(x) = −x2 − 9x + 10 shows the relationship between the vertical distance of a diver from a pool's surface f(x), in feet, and the horizontal distance x, in feet, of a diver from the diving board. What is a zero of f(x), and what does it represent?Group of answer choicesx = 1; the diver jumps in the pool at 1 foot per secondx = 10; the diver jumps in the pool at 10 feet per secondx = 1; the diver hits the water 1 foot away horizontally from the boardx = 10; the diver hits the water 10 feet away horizontally from the board

The height of a diver above the water, is given by , where is time measured in seconds and is measured in meters. Select all statements that are true about the situation.A:The diver begins 5 meters above the water.B:The diver begins 3 meters above the water.C:The function has 1 zero that makes sense in this situation.D:The function has 2 zeros that make sense in this situation.E:The graph that represents starts at the origin and curves upward.F:The diver begins at the same height as the water level.

ProblemSuppose Jeremiah is a diver for his summer swim team. The function h(x)=−4.9x2+8x+5ℎ(𝑥)=−4.9𝑥2+8𝑥+5 represents Jeremiah's height (hℎ) in meters above the water x𝑥 seconds after he leaves the diving board.What is the initial height of the diving board?At what time did Jeremiah reach his maximum height?What was Jeremiah’s maximum height?Sketch a graph of the function. (You can use your calculator for this or create a table of values.) SolutionThe initial height of the diving board is when the time is zero.h(0)=−4.9x2+8x+5ℎ(0)=−4.9𝑥2+8𝑥+5h(0)=−4.9(0)2+8(0)+5ℎ(0)=−4.9(0)2+8(0)+5h(0)=0+0+5ℎ(0)=0+0+5h(0)=5ℎ(0)=5The initial height of the diving board is 55 m.The time at which Jeremiah reaches his maximum height is the x𝑥-coordinate of the vertex.x=−b2a𝑥=−𝑏2𝑎x=𝑥=2(2( ))x=−8−9.8𝑥=−8−9.8x=0.82𝑥=0.82 secIt took Jeremiah seconds to reach his maximum height.The maximum height was reached Jeremiah at seconds. The maximum height is the y𝑦-coordinate of the vertex.h(t)=−4.9x2+8x+5ℎ(𝑡)=−4.9𝑥2+8𝑥+5h(0.82)=−4.9(0.82)2+8(0.82)+5ℎ(0.82)=−4.9(0.82)2+8(0.82)+5h(0.82)=−3.29+6.56+5ℎ(0.82)=−3.29+6.56+5h(0.82)=8.27ℎ(0.82)=8.27 mThe maximum height reached by Jeremiah was m.CheckQuestion 8

Jamieson is competing in his school’s 3.0-metre diving competition. For his last dive, he is performing a forward somersault. The duration of the dive must be exactly 1.75 seconds or he will under- or over-rotate before hitting the water. He jumps upwards off the board with a vertical velocity of 6.0 m s−1 and takes $t$t​ seconds to land in the pool. Take the upwards direction as positive.Which of the following correctly describes the displacement of the diver as he hits the water?A0 mB3.0 mC−3.0 mD6.0 m

A free-diver is training to dive deeper. They can currently dive to −12m⁡−12m. After 66 months they can dive 44 times deeper. Choose two equations that represent this scenario, where 𝑥x is the new depth the diver can reach.𝑥=4×−12x=4×−12𝑥=−124x= 4−12​ 𝑥4=−124x​ =−124𝑥=−124x=−12

A group of children are swimming in a pool. They start in the middle of the pool and swim 20 feet toward the right end of the pool. They then swim to a point x feet to the right of the middle of the pool. So far, the children have swum a distance of 45 feet. Formulate an absolute value equation to represent this situation. Then solve the equation. a; b; c; or d; or