How To Find The Maximum Value Of A Quadratic Function

For example if you re starting with the function f x 3x 2x x 2 3x 2 4 you would combine the x 2 and x terms to simplify and end up with f x 2x 2 5x 4. The maximum and minimum value of f occurs at x h.

Determine If A Quadratic Has A Max Or Min Value Then Find It

If the parabola is open upward then it will have minimum value.

How to find the maximum value of a quadratic function. Maximum value of a quadratic function the quadratic function f x ax2 bx c will have only the maximum value when the the leading coefficient or the sign of a is negative. Y a x h 2 k. The maximum value would be equal to infinity.

When a is negative the graph of the quadratic function will be a parabola which opens down. Minimum value of parabola. The maximum value of the function is an area of 800 square feet which occurs when displaystyle l 20 l 20 feet.

Once you have identified the coefficients you can use a formula to find the x coordinate and the y coordinate for the minimum or maximum value of the quadratic equation. If value of a is negative. The minimum value would be equal to infinity.

The minimum value of the function will come when the first part is equal to zero because minimum value of a square function is zero. In order to find the maximum or minimum value of quadratic function we have to convert the given quadratic equation in the above form. If the x 2 coefficient is positive the function has a minimum.

The maximum value is y coordinate at the vertex of the parabola. Let f be a quadratic function with standard form. Determine whether the function will have a minimum or a maximum depending on the coefficient of the x 2 term.

To find the maximum or minimum value of a quadratic function start with the general form of the function and combine any similar terms. When the shorter sides are 20 feet there is 40 feet of fencing left for the longer side.

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