You are asked to find the minimum or maximum of the quadratic function: f (x) =3x^2+6x+1
What is the x-value of the minimum/maximum?
What is the y-value of the minimum/maximum?
Is this a minimum or maximum?
To find the minimum or maximum of a quadratic function, we need to find the vertex of the parabola. The x-value of the minimum/maximum is given by the formula: x = -b / (2a), where a = 3 and b = 6 in this case.
Plugging these values into the formula, we get:
x = -6 / (2*3) = -1
Now, we can find the y-value of the minimum/maximum by plugging this x-value back into the function:
f(-1) = 3*(-1)^2 + 6*(-1) + 1
f(-1) = 3 - 6 + 1
f(-1) = -2
Therefore, the x-value of the minimum/maximum is -1, the y-value is -2, and this is a minimum point since the coefficient of x^2 is positive, indicating a U-shaped parabola.