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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

Respuesta :

Hagrid
Setting f(x) = 0, we have:
-x2 -7x +30 =0

The roots of this quadratic equation are:
x = 3 and -10

Since the diver is on a diving board, the -10 is somewhere behind him. We use the root x = 3 since this distance is in front of the board.

Therefore, the answer is:
x = 3; the diver hits the water 3 feet away horizontally from the board

The diver hits the water 3 feet away horizontally from the board.

The correct option is (b)

What is Quadratic Equation?

A quadratic equation is a second-order polynomial equation in a single variable x,  ax²+bx+c=0 with a ≠ 0 .

Given function: f(x)= -x² -7x +30

Factorising f(x), we get

-x² -7x +30 =0

x² +7x -30 =0

x² +10x - 3x -30 =0

x(x+10)-3(x+10)=

(x+10)(x-3)=0

The roots of this quadratic equation are x = 3 and -10.

As, the diver is on a diving board we will not use -10.

Hence, the diver hits the water 3 feet away horizontally from the board.

Learn more about quadratic equation here:

https://brainly.com/question/2263981

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