Question
f (a, b) is the vertex of f (x) = -5x2 - 20x + 10,
hen what is the value of b?
hen what is the value of b?
Answers
GPT 3.5
To find the value of b, we first need to identify the coordinates of the vertex (a, b) in the equation f(x) = -5x^2 - 20x + 10.
The vertex of a quadratic function in the form f(x) = ax^2 + bx + c is given by the formula:
Vertex(a, b) = (-b/2a, f(-b/2a))
In our equation, a = -5 and b = -20.
Thus, the x-coordinate of the vertex is given by:
x = -(-20)/(2*(-5)) = 20/(-10) = -2
Now, substitute x = -2 into the equation to find the y-coordinate:
f(-2) = -5(-2)^2 - 20(-2) + 10
f(-2) = -5(4) + 40 + 10
f(-2) = -20 + 40 + 10
f(-2) = 30
Therefore, the vertex of the function is (-2, 30).
So, the value of b is 30.
The vertex of a quadratic function in the form f(x) = ax^2 + bx + c is given by the formula:
Vertex(a, b) = (-b/2a, f(-b/2a))
In our equation, a = -5 and b = -20.
Thus, the x-coordinate of the vertex is given by:
x = -(-20)/(2*(-5)) = 20/(-10) = -2
Now, substitute x = -2 into the equation to find the y-coordinate:
f(-2) = -5(-2)^2 - 20(-2) + 10
f(-2) = -5(4) + 40 + 10
f(-2) = -20 + 40 + 10
f(-2) = 30
Therefore, the vertex of the function is (-2, 30).
So, the value of b is 30.