g(x)=2x^2+20x+49, What is the function’s minimum or maximum value?

Answer 1

If you look at the graph of the function it's easier to see what the maximums and/or minimums are. The graph of g(x)=2x² + 20x + 49 looks like this:

From the graph you can see that this function has a minimum value. That minimum value is -1 and it occurs at x = -5.

For a quadratic (x-squared) function like this, the way to tell is the function will have a minimum or a maximum is to look at the leading term. In this case (when you put the function in order of largest exponent down to lowest), the leading term is 2x². If the leading term begins with a positive number (in this case +2), then the function will have a minimum value. If it had begun with a negative number (like maybe "-3" or just "-x²") then it would have a maximum value (the curve would be flipped over to look like a frowny face).

To find out where the minimum or maximum is, you use x = -b/(2a). "a" is the number in front of the "x²", "b" is the number in front of the "x", and "c" is the number at the end. Like this: ax² + bx + c so in this case, a = 2, and b = 20. So the minimum value will occur at:

x = -b/(2a)

x = -20/(2•2) = -20/4 = -5.

To find out what the minimum value is, we plug in x = -5 into the function like this:

g(x) = 2x² + 20x + 49

g(-5) = 2(-5)² + 20(-5) + 49

g(-5) = 2(25) + -100 + 49

g(-5) = 50 + -100 + 49

g(-5) = -1

So the minimum is at (-5, -1) in other word, the minimum occurs at x = -5 and is -1

Answer 2

To find the min or max value, you use the equation

x=-b/(2a)

b=20

a=2

x=-20/2(2)

x=-5

Once you have the x value, plug it into the original equation to get the y value

g(-5) = 2(-5)²+20(-5)+49

g(-5)=-1

To determine if it is a min or a max, look at the leading coefficient. If it is positive, the parabola opens up and there is a minimum. If it is negative, the parabola opens down and there is a maximum.

For this one, the leading coefficient is positive, the parabola opens UP and there is a minimum value

Answer 3

take the derivative, set it = 0, solve for x

4x+20 = 0

4x =-20

x = -20/4= -5

2(-5)^2 + 20(-5) + 49 =

50 -100 +49 = -1 = y

The point (-5,-1) ;is the minimum point and the vertex for a parabola opening upwards

there is no maximum, unless you want to say + infinity.

It just gets larger forever