Answer:
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 = [tex]\frac{-b}{2a}[/tex]
- Substitute the values of a and b
∴ h = [tex]\frac{-8}{2(-1)}=\frac{-8}{-2}[/tex]
∴ 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)
