An icicle drips at a rate that can be represented by the function f(x) = −x2 + 9x − 18, where 0 ≤ x ≤ 10 and x is the number of hours after the sun has risen. When f(x) is a negative number, the icicle is not dripping. Determine the values when the icicle starts and stops dripping.

x = −3 and x = 6
x = 3 and x = −6
x = 3 and x = 6
x = −3 and x = −6

[tex]f(x) = -x^2 + 9x - 18[/tex], where 0 ≤ x ≤ 10 and x is the number of hours after the sun has risen. So, The solution are x = 3 and x = 6.

What is a quadratic equation?

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

An icicle drips at a rate that can be represented by the function

[tex]f(x) = -x^2 + 9x - 18[/tex],

where 0 ≤ x ≤ 10 and x is the number of hours after the sun has risen.

First, we have to find its solution since it is a quadratic function;

[tex]f(x) = -x^2 + 9x - 18\\\\f(x) = -x^2 + 3x+ 6x - 18\\\\f(x) = x (3-x) - 6(3-x)\\\\f(x) = (3-x)(x-6)[/tex]

So, The solution are x = 3 and x = 6.

Learn more about quadratic equations;

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