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.
It if the max or minimum value.
A quadratic function is of the form: f(x) = ax2 + bx + c where a ≠0 If a > 0 then the quadratic has a minimum but its maximum, asymptotically, is +∞. If a < 0 then the quadratic has a maximum but its minimum, asymptotically, is -∞. The extremum (whichever it is) is attained when x = -b/2a. The extreme value is f(-b/2a) = a*(-b/2a)2 + b(-b/2a) + c = b2/4a - b2/2a + c = -b2/4a + c
Assuming the standard x and y axes, the range is the maximum value of y minus minimum value of y; and the domain is the maximum value of x minus minimum value of x.
pi value= 1
Surely, you should check the value of the function at the boundaries of the region first. Rest depends on what the function is.
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.
If x2 is negative it will have a maximum value If x2 is positive it will have a minimum value
It if the max or minimum 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)
· whether it is linear, quadratic or exponential · whether it has an upper or lower bound · whether it has a minimum or a maximum value · whether it is constant, decreasing or increasing
the maximum or minimum value of a continuous function on a set.
Both the function "cos x" and the function "sin x" have a maximum value of 1, and a minimum value of -1.
In Calculus, to find the maximum and minimum value, you first take the derivative of the function then find the zeroes or the roots of it. Once you have the roots, you can just simply plug in the x value to the original function where y is the maximum or minimum value. To know if its a maximum or minimum value, simply do your number line to check. the x and y are now your max/min points/ coordinates.
A quadratic function is of the form: f(x) = ax2 + bx + c where a ≠0 If a > 0 then the quadratic has a minimum but its maximum, asymptotically, is +∞. If a < 0 then the quadratic has a maximum but its minimum, asymptotically, is -∞. The extremum (whichever it is) is attained when x = -b/2a. The extreme value is f(-b/2a) = a*(-b/2a)2 + b(-b/2a) + c = b2/4a - b2/2a + c = -b2/4a + c
You cannot. The function f(x) = x2 + 1 has no real zeros. But it does have a minimum.
In a quadratic equation, the vertex (which will be the maximum value of a negative quadratic and the minimum value of a positive quadratic) is in the exact center of any two x values whose corresponding y values are equal. So, you'd start by solving for x, given any y value in the function's range. Then, you'd solve for y where x equals the middle value of the two x's given in the previous. For example:y = x24 = x2x = 2, -2y = (0)2y = 0Which is, indeed, the vertex of y = x2
If a quadratic function is 0 for any value of the variable, then that value is a solution.