Question

Determine the vertex of the quadratic relation y=2(x+2)(x-6).

Answer 1

vertex = (2, - 32 )

Explanation:

given a quadratic function in standard form

y = ax² + bx + c ( a ≠ 0 ) , then the x- coordinate of the vertex is

x = -
`(b)/(2a)`

given

y = 2(x + 2)(x - 6) ← expand factors using FOIL

= 2(x² - 4x - 12 ) ← distribute parenthesis

y = 2x² - 8x - 24 ← in standard form

with a = 2, b = - 8 , then

x = -
`(-8)/(4)` = 2

substitute x = 2 into the function for corresponding y- coordinate

y = 2(2 + 2)(2 - 6) = 2(4)(- 4) = 8 × - 4 = - 32

vertex = (2, - 32 )

Answer 2

The vertex is (2,-32)