Question

Worth 100 points so easy.

What is the vertex of the parabola?

f(x) = 2x² + 16x + 30
x=
y=

Answer 1

vertex = (- 4, - 2 )

Explanation:

given a parabola in standard form

f(x) = ax² + bx + c ( a ≠ 0 )

then the x- coordinate of the vertex is

`x_(vertex)` = -
`(b)/(2a)`

f(x) = 2x² + 16x + 30 ← is in standard form

with a = 2 , b = 16 , then

`x_(vertex)` = -
`(16)/(2(2))` = -
`(16)/(4)` = - 4

substitute x = - 4 into f(x) for corresponding y- coordinate

f(- 4) = 2(- 4)² + 16(- 4) + 30

= 2(16) - 64 + 30

= 32 - 34

= - 2

vertex = (- 4, - 2 ) or x = - 4 , y = - 2