Question

Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (x,y)(x,y) point.

Answer 1

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

• h = $\frac{-b}{2a}$
• k is the value of y at x = h

∵ 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 = $\frac{-b}{2a}$

- Substitute the values of a and b

∴ h = $\frac{-8}{2(-1)}=\frac{-8}{-2}$

∴ 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)