Question

Y = 3x² - 24x + 57

find the coordinates of the vertex

Answer 1

(4,9)

Explanation:

The word "vertex" isn't clear here. I'm assuming the question is referring to finding the stationary (turning) point. This can be found by finding the derivative (dy/dx).

To find the derivative we use the following formula:

`y = ax^(n)\\ (dy)/(dx) = nax^(n-1)`

What this means is that for each term of the equation, we multiply by the current power and then reduce the power by 1. In the case of the question's equation, this will be done like this:

`y = 3x^(2) - 24x + 57\\(dy)/(dx) = 6x - 24`

Now we can use this to find the stationary point, as stationary points are where the derivative (dy/dx) = 0:

6x - 24 = 0

6x = 24

x = 4

Through this we have found the x-coordinate of the stationary point, however we still need to find the y coordinate. This is done by substituting our x value back into the original equation (not the derivative):

y = 3(4)² - 24(4) + 57

y = 9

Therefore, the coordinates of the stationary point are (4,9)