Question

What is the vertex of the graph of y = 2x^2 + 4x − 5? (0, −5) (−1, −7) (1, 1) (2, 11)

Answer 1

vertex = (- 1, - 7 )

Explanation:

given a parabola in standard form

y = ax² + bx + c (a ≠ )

then the x- coordinate of the vertex is

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

y = 2x² + 4x - 5 ← is in standard form

with a = 2 , b = 4 , then

`x_(vertex)` = -
`(4)/(2(2))` = -
`(4)/(4)` = - 1

substitute x = - 1 into the equation for corresponding y- coordinate

y = 2(- 1)² + 4(- 1) - 5 = 2(1) - 4 - 5 = 2 - 9 = - 7

vertex = (- 1, - 7 )