Help! I don't know how to solve

An electronics store is deciding how to price one of its products. The equation P = -25d 2 + 50d predicts the total profit P as a function of the product's price in dollars d. What price will produce the highest total profit? (where is the vertex?)

P(d) = -25d(d-2)

the vertex is midway between the roots, at d=1
or, using the vertex form,
P(d) = -25(d^2-2d+1) +25 = -25(d-1)^2 + 25

Thank you so much!

To find the price that will produce the highest total profit, we first need to determine the vertex of the quadratic equation P = -25d^2 + 50d.

The vertex of a quadratic equation in the form of y = ax^2 + bx + c can be found using the formula: x = -b / (2a).

Comparing the equation P = -25d^2 + 50d to the standard form y = ax^2 + bx + c, we can see that a = -25 and b = 50.

Using the formula x = -b / (2a), we can substitute the values into the formula:

x = -50 / (2 * -25)
x = -50 / -50
x = 1

Therefore, the vertex of the equation P = -25d^2 + 50d is at the price d = 1.

The price that will produce the highest total profit is $1.

To find the price that will produce the highest total profit, we need to determine the vertex of the parabola represented by the equation P = -25d^2 + 50d.

The vertex of a parabola in the form of y = ax^2 + bx + c can be found using the formula: x = -b / (2a).

In our case, the equation is P = -25d^2 + 50d, so a = -25 and b = 50.

Now let's substitute these values into the formula:
d = -50 / (2*-25)

Simplifying this expression, we have:
d = -50 / (-50)
d = 1

So, the price that will produce the highest total profit is $1, which corresponds to the vertex of the parabola.