Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (x, y)(x, y) point.
y=-x^2+8x
PLEASE HELP

The coordinates of the vertex are (4 , 16)

Step-by-step explanation:

The coordinates of the vertex of a parabola which represents a quadratic equation y = ax² + bx + c are (h , k), where

∵ The equation of the parabola is y = - x² + 8x

- Compare it by the form of the equation above to find a, b and c

∵ a is the coefficient of x²

∴ a = -1

∵ b is the coefficient of x

∴ b = 8

∵ c is the numerical term

∴ c = 0

The vertex of the parabola is (h , k)

∵ h =

- Substitute the values of a and b

∴ h =

∴ h = 4

∵ k = y at x = h

- Substitute x by 4 and y by k in the equation

∵ k = - (4)² + 8(4)

∴ k = -16 + 32

∴ k = 16

∴ The coordinates of the vertex are (4 , 16)

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.