The function f(x) = −x2 − 7x + 30 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?

x = 10; the diver hits the water 10 feet away horizontally from the board.
x = 3; the diver hits the water 3 feet away horizontally from the board.
x = 10; the diver jumps in the pool at 10 feet per second.
x = 3; the diver jumps in the pool at 3 feet per second.

Question

The function f(x) = −x2 − 7x + 30 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?

x = 10; the diver hits the water 10 feet away horizontally from the board.
 x = 3; the diver hits the water 3 feet away horizontally from the board.
 x = 10; the diver jumps in the pool at 10 feet per second.
 x = 3; the diver jumps in the pool at 3 feet per second.

darkknight · Answer

Zeros of the function where the function crosses the x-axis, so factor out the function f(x) and see where x = 0

yayitsofia · Answer

so like whats the answer or how do i factor it

darkknight · Answer

$$-x^2-7x+30=-(x^2+7x-30)=-(x+10)(x-3)$$
based off of this your zeros are...?

yayitsofia · Answer

1?

darkknight · Answer

Buddy, where do you get 1 from, Read please ._.

yayitsofia · Answer

30????

SmokeyBrown · Answer

darkknight showed that you can factor the equation into
(-)(x+10) multiplied by (x-3)
If either term (x+10) or (x-3) is equal to 0, then the result of the equation is 0.
So, what would x have to be, in order for (x+10) to be 0? That's one of the "zeros". Likewise, what would x have to be in order for (x-3) to be 0? That's the other "zero"