select the approximate value of x that are solutions to f(x)=0 where f(x)= -5x^2+6x+9

At vertex, x=6/10=0.6

Try
f(-1)=-2
f(0)=9
f(2)=-1
So -1 and +2 could be approximate zeroes of f(x).

on 16 of 20

5.0 Points
The local zoo has two water tanks for the elephant exhibit that are leaking One water tank contains 12 gal of water and is leaking at a constant rate of 3 gal/h. The second water tank contains 8 gal of water and is leaking at a constant rate of 5 gal/h. When will the two tanks have the same amount of water? Explain. Let x = the number of hours the tanks are filling and let y = the number of gallons in the tank.

To find the approximate values of x that are solutions to the equation f(x) = 0, where f(x) = -5x^2 + 6x + 9, we can use the quadratic formula.

The quadratic formula is given by:

x = (-b ± sqrt(b^2 - 4ac)) / (2a)

For our equation f(x) = -5x^2 + 6x + 9, we have:
a = -5, b = 6, and c = 9.

Now, plug these values into the quadratic formula:

x = (-6 ± sqrt(6^2 - 4(-5)(9))) / (2(-5))

Simplifying this equation gives:

x = (-6 ± sqrt(36 + 180)) / (-10)
x = (-6 ± sqrt(216)) / (-10)
x = (-6 ± 14.6969) / (-10)

Now we can calculate the approximate values of x:

x₁ = (-6 + 14.6969) / (-10) = 0.5697
x₂ = (-6 - 14.6969) / (-10) = 2.5697

Therefore, the approximate values of x that are solutions to the equation f(x) = 0 are x = 0.5697 and x = 2.5697.