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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?

A) x = 10; the diver hits the water 10 feet away horizontally from the board.

B) x = 3; the diver hits the water 3 feet away horizontally from the board.

C) x = 10; the diver jumps in the pool at 10 feet per second.

D) x = 3; the diver jumps in the pool at 3 feet per second.

Respuesta :

nobillionaireNobley
A zero of a function is the value of x when the function equals zero.
Here, when f(x) = 0
0 = -x^2 - 7x + 30
x^2 + 7x - 30 = 0
x^2 - 3x + 10x - 30 = 0
x(x - 3) + 10(x - 3) = 0
(x + 10)(x - 3) = 0
x + 10 = 0 or x - 3 = 0
x = -10 or x = 3
but the horizontal distance cannot be zero,
therefore, x = 3 and it means that the diver hits the water 3 feet away horizontally from the board.



facundo3141592

The positive zero of the quadratic function is x = 3, this means that he hits the water at 3 ft from the board.

What is a zero of f(x), and what does it represent?

Here we have the quadratic function:

[tex]f(x) = -x^2 - 7x + 30[/tex]

The zeros are given by the Bhaskara's formula, it gives:

[tex]x = \frac{7 \pm \sqrt{(-7)^2 - 4*(-1)*30} }{2*-1} \\\\x = \frac{7 \pm 13}{-2}[/tex]

Then there are two zeros:

x = (7 + 13)/-2 = -10

x = (7 - 13)/-2 = 3

We only care about the positive solution, x = 3.

Because f(x) represents vertical distance, f(0) means that the diver is in the surface of the water.

So the correct option is B.

If you want to learn more about quadratic equations:

https://brainly.com/question/1214333

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