Answer:
Minimum value = -6
Explanation:
The minimum value is the y-coordinate of the minimum on the parabola.
Currently 3/4x^2 + 6x + 6 is in standard form, whose general equation is:
ax^2 + bx + c
Step 1: We can first find the x-coordinate of the maximum using the following formula:
-b / 2a
From the function, we see that 6 is b and 3/4 is a. Now, we plug these values into the formula and simplify:
-6 / (2 * 3/4)
-6 / (6/4)
-6 / (3/2)
-6 * 2/3
-12/3
-4
Step 2: Now we can plug in -4 for x in the function to find the minimum value:
y = 3/4(-4)^2 + 6(-4) + 6
y = 3/4(16) -24 + 6
y = 48/4 - 24 + 6
y = 12 - 24 + 6
y = -12 + 6
y = -6
Thus, the minimum value of the function y = 3/4x^2 + 6x + 6 is -6