How to find the least value of a quadratic equation?

How to find the least value of a quadratic equation?

To find the least value of a quadratic equation, you can use the vertex form of the equation. The vertex form is given by y = a(x – h)^2 + k, where (h, k) is the vertex of the parabola. The least value of the quadratic equation occurs at the vertex of the parabola.

To find the least value, you can follow these steps:
1. Identify the values of a, h, and k in the vertex form of the quadratic equation.
2. Substitute the values of a, h, and k into the equation to find the coordinates of the vertex.
3. The y-coordinate of the vertex is the least value of the quadratic equation.

By following these steps, you can easily determine the least value of a quadratic equation.

FAQs

1. What is a quadratic equation?

A quadratic equation is a second-degree polynomial equation in one variable. It has the general form ax^2 + bx + c = 0, where a, b, and c are constants.

2. What is the vertex form of a quadratic equation?

The vertex form of a quadratic equation is y = a(x – h)^2 + k, where (h, k) is the vertex of the parabola.

3. How do you find the vertex of a quadratic equation?

To find the vertex of a quadratic equation, you can use the formula h = -b/2a and then substitute the value of h back into the equation to find k.

4. What is the significance of the vertex in a quadratic equation?

The vertex of a quadratic equation represents either the maximum or minimum value of the parabola. It is also the point where the parabola changes direction.

5. How do you determine if the vertex is the minimum or maximum value?

If the coefficient of x^2 (a) is positive, the vertex represents the minimum value of the parabola. If a is negative, the vertex represents the maximum value.

6. Can a quadratic equation have no minimum value?

Yes, if the coefficient of x^2 (a) is negative, the quadratic equation has no minimum value. It will have a maximum value instead.

7. Can a quadratic equation have more than one minimum value?

No, a quadratic equation has only one minimum or maximum value, which is determined by the vertex of the parabola.

8. How do you graph a quadratic equation to visualize the minimum value?

Plot the vertex of the parabola, which represents the minimum value, and then sketch the curve of the parabola. The lowest point of the curve will correspond to the minimum value of the quadratic equation.

9. What is the relationship between the discriminant and the minimum value of a quadratic equation?

The discriminant (b^2 – 4ac) in a quadratic equation can help determine if the parabola opens upwards (positive discriminant, minimum value) or downwards (negative discriminant, maximum value).

10. Can a quadratic equation have an infinite minimum value?

No, a quadratic equation cannot have an infinite minimum value. It will have a finite minimum value, which is determined by the vertex of the parabola.

11. How do you compare the minimum values of two different quadratic equations?

To compare the minimum values of two quadratic equations, find the vertices of both equations and compare their y-coordinates. The equation with the smaller y-coordinate has the lower minimum value.

12. Can the least value of a quadratic equation be negative?

Yes, the least value of a quadratic equation can be negative if the vertex is located below the x-axis. This indicates that the parabola opens downwards, and the vertex represents a maximum value.

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