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?
A: x = 1; the diver jumps in the pool at 1 foot per second
B: x = 10; the diver jumps in the pool at 10 feet per second
C: x = 1; the diver hits the water 1 foot away horizontally from the board
D: x = 10; the diver hits the water 10 feet away horizontally from the board

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whitneytr12 whitneytr12 · Answer 1 · 2019-11-07T16:50:56+01:00

Answer:

Zeros of a function: x = 1 and x = -10

Step-by-step explanation:

A zero of a function is the value of x when f(x) = 0. In other words it is the intersect point between x and y=f(x), when y =0.

First we need to make f(x)=0, so we would have: [tex] -x^{2}-9x+10=0 [/tex].

If we factorize this quadratic function, we would have: [tex](x+10)(x-1)=0[/tex]

So we get x = -10 and x = 1.

x = 1 means that the diver hits the water 1 foot away horizontally from the board.
x=-10 means the diver hits the water 10 feet behind the diving board.

Hope it helps!