Calculates the maximum and minimum values of quadratic functions.
Author: shiroeExecutions: 4983
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Calculates the maximum and minimum values of a quadratic function. The domain is a closed interval. Calculates the maximum and minimum values in the corresponding range.
Consider the graph of a quadratic function in the xy-plane. The curve is a parabola.
Let y = f(x), where f(x) = ax² + bx + c.
Assume the domain is a closed interval.
Let L be the minimum value in the domain. Let R be the maximum value in the domain.
Calculate the maximum and minimum values of the range with respect to the domain.
Enter a non-zero value for a. If 0 is entered, it will be converted to 1.
Enter real numbers for the coefficients and constant term: a, b, and c.
Enter different values for L and R. Assume that R is greater than L.
L and R are real numbers.
Here, the position of the axis refers to the x-coordinate of the vertex of the parabola.
If an axis were to be drawn, it would be the x-coordinate of the intersection point with the x-axis.
The program determines whether the axis position lies within the domain. In the output field “Is the axis position within the domain?”,
it displays 1 if it is within the domain and 0 if it is outside.
It examines the relationship between the axis position and the domain. In the output field “Relationship between the axis and the domain”,
it displays -1 if the axis position is on the negative side of the x-axis relative to the domain(the axis position is less than L),
0 if the axis position is within the domain,
and 1 if the axis position is to the positive side of the x-axis relative to the domain (the axis position is greater than R).
x1 and x2 are the solutions to the quadratic equation f(x) = 0 and are provided for reference.
Since the output values are complex numbers and the imaginary part is not necessarily 0,
please check to make sure the imaginary unit i is not appended to the end of the number.
Let y = f(x), where f(x) = ax² + bx + c.
Assume the domain is a closed interval.
Let L be the minimum value in the domain. Let R be the maximum value in the domain.
Calculate the maximum and minimum values of the range with respect to the domain.
Enter a non-zero value for a. If 0 is entered, it will be converted to 1.
Enter real numbers for the coefficients and constant term: a, b, and c.
Enter different values for L and R. Assume that R is greater than L.
L and R are real numbers.
Here, the position of the axis refers to the x-coordinate of the vertex of the parabola.
If an axis were to be drawn, it would be the x-coordinate of the intersection point with the x-axis.
The program determines whether the axis position lies within the domain. In the output field “Is the axis position within the domain?”,
it displays 1 if it is within the domain and 0 if it is outside.
It examines the relationship between the axis position and the domain. In the output field “Relationship between the axis and the domain”,
it displays -1 if the axis position is on the negative side of the x-axis relative to the domain(the axis position is less than L),
0 if the axis position is within the domain,
and 1 if the axis position is to the positive side of the x-axis relative to the domain (the axis position is greater than R).
x1 and x2 are the solutions to the quadratic equation f(x) = 0 and are provided for reference.
Since the output values are complex numbers and the imaginary part is not necessarily 0,
please check to make sure the imaginary unit i is not appended to the end of the number.
| a's adopted value | |
| The value adopted for b | |
| Adopted values for c | |
| Adopted values for L | |
| R's Adopted Numeric Values | |
| Maximum value | |
| Minimum value | |
| f(L) | Endpoint values for L |
| f(R) | Endpoint values for R |
| Axis | The position of the axis (equal to the x-coordinate of the vertex of the parabola). |
| Height of a vertex | The y-coordinate of the vertex of a parabola. |
| If a is positive, return 1; if negative, return -1. | If a is positive, the parabola is concave downward. If a is negative, it is concave upward. |
| Whether the axis position lies within the domain | Return 1 if the axis is within the domain; 0 otherwise. |
| Relationship Between the Axis and the Domain | For the x-coordinate, display -1 if the point lies to the left of R on the axis, 0 if it lies within the domain, and 1 if it lies to the right of L. |
| Reference: x1 | For reference: Solution 1. |
| Reference: x2 | For reference: Solution #2. |
R5 (2023). Dec. 10 (Sun)_2-hour interval_max, min_Ver. 001
fukusosu, keta50, keta_kahen
fukusosu, keta50, keta_kahen
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