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Identify the minimum value of the function y = 3/4x^2+6x+6

User Miquelvir
by
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1 Answer

2 votes

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

User Mbnx
by
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