SOLUTION: what is the maximum or minimum value of the quardratic function ? f(x)=3x^2+12x+8 a. -28 b. -4 c. -2 d. 44 tthanks!

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: what is the maximum or minimum value of the quardratic function ? f(x)=3x^2+12x+8 a. -28 b. -4 c. -2 d. 44 tthanks!      Log On


   

Question 308022: what is the maximum or minimum value of the quardratic function ?
f(x)=3x^2+12x+8
a. -28
b. -4
c. -2
d. 44
tthanks!
Found 2 solutions by Fombitz, rapaljer:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
You can either differentiate and find when the derivative is zero.
f(x)=3x%5E2%2B12x%2B8+
f'(x)=6x%2B12=0+
x=-2+
f%28-2%29=3%284%29%2B12%28-2%29%2B8+
f%28-2%29=12-24%2B8=-4+
Use the second derivative to find whether its min or max.
f''(x)=6%3E0+
Since the second derivative is positive, the value is a minimum.
.
.
.
Or algebraically complete the square to find the vertex form,
f%28x%29=3x%5E2%2B12x%2B8+
f%28x%29=3%28x%5E2%2B4x%29%2B8+
f%28x%29=3%28x%5E2%2B4x%2B4%29%2B8-12+
+f%28x%29=3%28x%2B2%29%5E2-4+
Since the x%5E2 coefficient is positive (3), the parabola opens upwards and the value at the vertex is a minimum and occurs at (-2,-4).
.
.
.
b) is the correct answer.

Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
The maximum or minimum of a quadratic function occurs when x=-b/2a.
In this case, a=3, b=12, so x=-12/6=-2.

f(-2)=3(-2)^2+12(-2)+8
f(-2)=3*4+(-24)+8
f(-2)=12+(-16)=-4 = minimum value of f(x).

Are graphing calculators allowed???

Dr. Robert J. Rapalje, Retired