Question

When given a function in standard form,how can you determine if the parabola has aminimum or maximum value

Answer 1

Answer:

It can be determined if a quadratic function given in standard form has a minimum or maximum value from the sign of the coefficient "a" of the function. A positive value of "a" indicates the presence of a minimum point while a negative value of "a" indicates the presence of a maximum point

Step-by-step explanation:

The function that describes a parabola is a quadratic function

The standard form of a quadratic function is given as follows;

f(x) = a·(x - h)² + k, where "a" ≠ 0

When the value of part of the function a·x² after expansion is responsible for the curved shape of the function and the sign of the constant "a", determines weather the the curve opens up or is "u-shaped" or opens down or is "n-shaped"

When "a" is negative, the parabola downwards, thereby having a n-shape and therefore it has a maximum point (maximum value of the y-coordinate) at the top of the curve

When "a" is positive, the parabola opens upwards having a "u-shape" and therefore, has a minimum point (minimum value of the y-coordinate) at the top of the curve.