You are asked to find the minimum or maximum of the quadratic function: f (x) =3x^2+6x+1
What is b?
what is a?
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 the quadratic function f(x) = 3x^2 + 6x + 1, we first need to identify the values of a, b, and c in the standard form of a quadratic equation: ax^2 + bx + c.
Here, a = 3, b = 6, and c = 1.
To find the x-value of the minimum or maximum, we can use the formula x = -b / (2a). Plugging in the values of a and b, we get:
x = -6 / (2*3) = -6 / 6 = -1.
To find the y-value of the minimum or maximum, we substitute the x-value back into the original function:
f(-1) = 3*(-1)^2 + 6*(-1) + 1 = 3 - 6 + 1 = -2.
Since the coefficient of the x^2 term is positive (a = 3), the quadratic function opens upwards and has a minimum value at the point (-1, -2).
Therefore, b = 6, a = 3, x-value of the minimum = -1, y-value of the minimum = -2, and this point represents the minimum of the quadratic function.