Question

What is the vertex form of # f(x) = -5x^2-4x+9 #?

Answer 1

x-coordinate of vertex:
`x = -b/(2a) = 4/-10 = -2/5`
y-coordinate of vertex:
`y(-2/5) = - 5(4/25) + 4(2/5) + 9 = -4/5 + 8/5 + 9 = 49/5`
Vertex `(-2/5, 49/5)`
Vertex form of f(x):
`f(x) = -5(x + 2/5)^2 + 49/5`
graph{- 5x^2 - 4x + 9 [-10, 10, -5, 5]}
graph{- 5x^2 - 4x + 9 [-20, 20, -10, 10]}