Question 350825: how do you figure out the height of the max/min when drawin a quadratic parobola???
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! x = -b /2a is the formula to get the x value of the maximum / minimum
once you get that, then you get f(-b/2a) to get the y value.
the point pair (x,f(x)) becomes (-b/2a, f(-b/2a)) becomes the maximum / minimum point.
if the coefficient of the x^2 term is positive, then the max/min point is a minimum point.
if the coefficient of the x^2 term is negative, then the max/min point is a maximum point.
some examples:
y = f(x) = x^2 + 2x + 3
the equation is in standard form of ax^2 + bx + c, so:
a = 1
b = 2
c = 3
x value of max/min point is x = -b/2a which becomes -2/2 which becomes -1.
the y value of max/min point is y = f(x) = f(-b/2a) = f(-1).
since f(x) = x^2 + 2x + 3, then f(-1) = (-1)^2 + 2*(-1) + 3 which becomes 1 - 2 + 3 which becomes 2.
the max/min point becomes (-1,2) which means that x = -1, and y = 2.
coefficient of x^2 term is positive, so this is a min point.
graph of this equation is shown below:
you can see that the max/min point is at (-1,2), and that this is a min point because the coefficient of the x^2 term is positive.
take the same equation and make the coefficient of the x^2 term negative.
you get:
y = f(x) = -x^2 + 2x + 3
x value of max/min point is still x = -b/2a, only in this case:
a = -1
b = 2
c = 3
x = -b/2a becomes -2/-2 = 1
y value of max/min point = f(x) = f(-b/2a) = f(1) = -(1)^2 + 2*1 + 3 = -1 + 2 + 3 = 4
max/min point becomes (x,y) = (1,4) where x value is equal to 1 and y value is equal to 4.
graph of this equation is shown below:
you can see that the max/min point is at (x,y) = (1,4) and that the max/min point is a maximum because the coefficient of the x^2 term is negative.
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