Find the vertex for the parabola given by the function ƒ(x) = −3x^2 − 6x.A) (1, 3) B) (−1, 3) C) (−1/2, 2) D) (−1/2, 3)
Accepted Solution
A:
Answer:B) (−1, 3) Step-by-step explanation:The standard form of a quadratic function is y = ax² + bx + c
The vertex form of a parabola is
y = a(x - h)² + k
where (h, k) is the vertex of the parabola.
h = -b/(2a) and k = f(h)
In your equation, ƒ(x) = −3x² − 6x
a = -3; b = -6; c = 0
Calculate h
h = -(-6)/2(-3)]
h = 6/(-6)
h = -1
Calculate k
k = -3(-1)² -6(-1)
k = -3 + 6
k = 3
So, h = -1, k = 3, a = -3
The vertex form of the equation is f(x) = -3(x + 1)² + 3.
The vertex is at (-1, 3).
The figure below shows the graph of ƒ(x) = −3x² − 6x with the vertexat (-1, 3).