Question 328150: How would I determine whether the functionc have a minimum or maximum value and then find the value?
g(x)=-4x^2+8x+3
Answer by nyc_function(2741)   (Show Source):
You can put this solution on YOUR website! Look at the number next to x^2. If it is positive, the parabola opens upward and you have minimum value. If the number is negative (as we see here), then the parabola opens downward and we have maximum value.
The value that you seek is called the vertex of the parabola.
We use x = -b/2a to find the x value of the vertex.
Let a = -4
Let b = 8
Do you see where I found a and b? Look at your function carefully.
x = -8/2(-4)
x = -8/-8
x = 1
To find the y value of your vertex, replace every x that you see in the function with 1 and solve for y.
Let g(x) = y
y = -4(1)^2 + 8(1) + 3
y = -4 + 8 + 3
y = -4 + 11
y = 7
The vertex here is the point (1,7).
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