Question

What are the cooridinates of the vertex of the parabola y=-5x^2+30x-25

Answer 1

vertex = (3, 20 )

Explanation:

given a parabola in standard form

y = ax² + bx + c ( a ≠ 0 )

the x- coordinate of the vertex is

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

y = - 5x² + 30x - 25 ← is standard form

with a = - 5 and b = 30 , then

`x_(vertex)` =
`(-30)/(2(-5))` =
`(-30)/(-10)` = 3

substitute x = 3 into the equation for the corresponding y- coordinate

y = - 5(3)² + 30(3) - 25

= - 5(9) + 90 - 25

= - 45 + 65

= 20

coordinates of vertex = (3, 20 )