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?

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Tutorconsortium365 Tutorconsortium365 · Answer 1 · 2022-08-18T06:13:09+02:00

The positive zero of the given quadratic function is x = 3. It represents that the diver hits the water at 3 feet from the board.

Quadratic equation refers to a function that is of the form: [tex]ax^{2}+bx+c; a\neq 0[/tex] .

The zeroes of a quadratic function refers to the points, where the graph of the equation cuts the x-axis, i.e., [tex]ax^{2}+bx+c=0[/tex] will give us the zeroes of the given quadratic function.

Now, for the quadratic function: [tex]-x^{2}-7x+30[/tex], the zeroes of the equation, given by Bhaskara's formula, are:

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

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

We only care about the positive zero, i.e., x = 3.

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

Thus, f(0) = 3 represents that the diver is still at the surface of the water and hits the water surface at a distance 3 feet from the board.

To know more about quadratic functions from the given link:

https://brainly.com/question/1214333

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