SOLUTION: Find the maximum or minimum value of the function. f(x) = 2x^2 + 3x + 1 Can you please show me how to figure this problem out? I would greatly appreciate it. Thank you very m

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Question 203074This question is from textbook
: Find the maximum or minimum value of the function.
f(x) = 2x^2 + 3x + 1
Can you please show me how to figure this problem out? I would greatly appreciate it. Thank you very much for you time and your help.
Brenda This question is from textbook

Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!
Functions of the form: g(x) = ax^2 + bx + c are (vertically oriented) parabolas. And I hope you know what parabolas look like. They are somewhat u-shaped (or upside-down u-shaped).

Your function is of this form, with a = 2, b = 3 and c = 1. So your function is a parabola.

The bottom of the "U" (or, for the upside-down ones, the top of the "U") is called the vertex. The vertex of a parabola with be the maximum or minimum value, depending on whether the "U" is right-side up or upside-down.

So the problem you have is to:
  1. Find the vertex of the parabola.
  2. Determine if the parabola is right-side up or upside down.
  3. Use the answer of #2 to determine if the vertex is a maximum or minimum,

1. Find the vertex. The vertex of the parabola will be when the x-value is -b/(2a). Your b is 3 and your a is 2 so the x-value of the vertex will be . Now we use this x-value to find the function value (the y-value) for the vertex: . So the vertex is (-3/4, -1/8).

2. Determine if the parabola is right-side up or upside-down. If a > 0 then the parabola is right-side up. If a < 0 then the parabola is upside-down. Your a is 2 so your parabola is right-side up.

3. Determine if the vertex is a maximum or a minimum value. Since the parabola is right-side up, the vertex is the bottom of the "U". So the vertex is a minimum value.

The minimum value for f(x) is -1/8 (when x = -3/4).
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