the path of a cliff diver as he dives into a lake is given by the equation y=-(x-10)power of 2 + 75...where y meters is the divers height above the water and x metres is the horizontal distance travelled by the diver. what is the maximum height the diver is above the water?

y = -(10-x)^2+75

This is just a parabola with vertex at (10,75)

So, the max height is 75 meters

Well, let me put on my scuba gear and dive right into the answer!

In this equation, y represents the diver's height above the water and x represents the horizontal distance traveled. The equation y = -(x - 10)^2 + 75 is a quadratic equation in vertex form. The vertex of a quadratic function is the maximum or minimum point.

In this case, the negative sign in front of the quadratic term implies that the function is concave downwards, which means the vertex represents the maximum point.

The x-coordinate of the vertex (h) can be found by setting the equation inside the parentheses equal to zero, so x - 10 = 0, which gives us x = 10.

Now, let's substitute the value of x = 10 into the equation to find the maximum height (y):

y = -(10 - 10)^2 + 75
y = -0^2 + 75
y = 75

Therefore, the maximum height the diver reaches above the water is 75 meters. So, don't forget to make a big splash and add some pizzazz to your dive!

To find the maximum height the diver is above the water, we need to determine the vertex of the parabolic equation. The general form of a parabola is y = ax^2 + bx + c, where "a" is the coefficient of the squared term, "b" is the coefficient of the linear term, and "c" is the constant term.

In this equation, y = -(x - 10)^2 + 75, we can see that "a" is -1, "b" is 20 (-1 * -10 * 2), and "c" is 75.

The x-coordinate of the vertex can be found using the formula x = -b/(2a).

Substituting the values into the formula, we get:
x = -20 / (2 * -1)
x = 20 / 2
x = 10

So, the x-coordinate of the vertex is x = 10.

To find the maximum height (y-coordinate) of the vertex, substitute x = 10 into the equation:
y = -(10 - 10)^2 + 75
y = -0^2 + 75
y = 75

Therefore, the maximum height the diver is above the water is 75 meters.

To find the maximum height the diver reaches above the water, we need to determine the vertex of the parabolic equation.

The given equation for the path of the diver is y = -(x - 10)^2 + 75, where y represents the height above the water and x represents the horizontal distance traveled by the diver.

The vertex form of a parabolic equation is given by y = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola.

Comparing this with the given equation, we can determine that the vertex is at (h, k) = (10, 75).

Therefore, the maximum height the diver reaches above the water is 75 meters.