Y=3(x-5)(x-17)vertex and maximum or minimum and maximum or minimum value

Answer 1

To find the vertex of this quadratic function, we need to first expand it:

Y = 3(x² - 22x + 85)

Y = 3x² - 66x + 255

Now we can find the x-coordinate of the vertex by using the formula:

x = -b/2a

Where a = 3 and b = -66.

x = -(-66)/2(3) = 11

So the x-coordinate of the vertex is 11. To find the y-coordinate, we can substitute this value back into the original equation:

Y = 3(11)² - 66(11) + 255 = 48

So the vertex of the function is (11, 48).

To determine whether this function has a maximum or minimum value, we need to look at the coefficient of the x² term. Since this coefficient is positive (a = 3), the function has a minimum value.

Finally, we can find this minimum value by substituting the x-coordinate of the vertex into the original equation:

Y = 3(11)² - 66(11) + 255 = 48

So the minimum value of this function is 48.