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How to compute the minimum and maximum function values of a quadratic function?
Wiki User
∙ 11y ago
Suppose you have a quadratic function of the form
y = ax2 + bx + c where a, b and c are real numbers and a is non-zero. [If a = 0 it is not a quadratic!]
The turning point for this function may be obtained by differentiating the equation with respect to x, or by completing the squares. However you get there, the turning point is the solution to 2ax + b = 0 or x = -b/2a
Now,
if a > 0 then the quadratic has a minimum at x = -b/2a and it has no maximum because y tends to +∞ as x tends to ±∞ .
if a < 0 then the quadratic has a maximum at x = -b/2a and it has no minimum because y tends to -∞ as x tends to ±∞.
You evaluate the value of y at this point.
y = a(-b/2a)2 + b(-b/2a) + c
= b2/4a - b2/2a + c
= -b2/4a + c
= -(b2 - 4ac)/4a
In either case, if the domain of the function is bounded on both sides, then the missing extremum will be at one or the other bound - whichever is further away from (-b/2a).
Wiki User
∙ 11y ago
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How do you compute for the range?
Range = maximum - minimum
Can a quadratic functions have a maximum and a minimum?
Yes
How do you know if a quadratic has a minimum or maximum value?
When the quadratic is written in the form: y = ax2 + bx + c then if a > 0 y has a minimum if a < 0 y has a maximum and if a = 0 y is not a quadratic but y = bx + c, and it is linear. The maximum or minimum is at x = -b/(2a)
How do you determine if the graph of a quadratic function has a min or max from its equation?
If x2 is negative it will have a maximum value If x2 is positive it will have a minimum value
Maximum and minimum values of quadratic formula?
maximum and minimum are both (-b/2a , c - (b^2/4a))
What is the maximum and minimum of quadratic function parent function?
The minimum is the vertex which in this case is 0,0 or the origin. There isn't a maximum.....
How do you determine wheather a quadratic function has a maximum or minimum and how do you find it?
In theory you can go down the differentiation route but because it is a quadratic, there is a simpler solution. The general form of a quadratic equation is y = ax2 + bx + c If a > 0 then the quadratic has a minimum If a < 0 then the quadratic has a maximum [and if a = 0 it is not a quadratic!] The maximum or minimum is attained when x = -b/2a and you evaluate y = ax2 + bx + c at this value of x to find the maximum or minimum value of the quadratic.
How can a quadratic function have both a maximum and minimum point?
It can't - unless you analyze the function restricted to a certain interval.
What name is given to the turning point also known as the maximum or minimum of the graph of a quadratic function?
vertex
How do you compute for the range?
Range = maximum - minimum
Can a quadratic functions have a maximum and a minimum?
Yes
How do you tell if a quadratic function is minimum value or a maximum vale?
Standard notation for a quadratic function: y= ax2 + bx + c which forms a parabola, a is positive , minimum value (parabola opens upwards on an x-y graph) a is negative, maximum value (parabola opens downward) See related link.
How do you know if a quadratic has a minimum or maximum value?
When the quadratic is written in the form: y = ax2 + bx + c then if a > 0 y has a minimum if a < 0 y has a maximum and if a = 0 y is not a quadratic but y = bx + c, and it is linear. The maximum or minimum is at x = -b/(2a)
How do you determine if the graph of a quadratic function has a min or max from its equation?
If x2 is negative it will have a maximum value If x2 is positive it will have a minimum value
What is the maximum or minimum of a quadratic equation called?
The vertex.
What is maximum or minimum of function?
Addition is the maximum or minimum function in math.
Maximum and minimum values of quadratic formula?
maximum and minimum are both (-b/2a , c - (b^2/4a))
