Question

Determine the vertex of the quadratic function f(×)=2ײ-12×+11.

Answer 1

vertex = (3, - 7 )

Explanation:

given a quadratic function 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 - 12x + 11 ← is in standard form

with a = 2 and b = - 12 , then

`x_(vertex)` = -
`(-12)/(2(2))` = -
`(-12)/(4)` = - (- 3) = 3

to find the corresponding y- coordinate substitute x = 3 into f(x)

f(3) = 2(3)² - 12(3) + 11

= 2(9) - 36 + 11

= 18 - 25

= - 7

then vertex = (3, - 7 )