Final answer:
To find the minimum of a quadratic function, use the vertex formula x = -b / (2a), as this provides the x-coordinate of the minimum point on the parabola. Option a) is the correct choice for finding the minimum value.
Step-by-step explanation:
To find the minimum point of a quadratic function, you should:
- Identify the vertex by using the formula x = -b / (2a). This will give you the x-coordinate of the vertex of the parabola. Since a quadratic function is in the form of ax² + bx + c, by finding the vertex, you can determine the lowest (or highest) point on the graph, known as the minimum (or maximum if a is negative) value.
- The discriminant is not useful in finding the minimum value, as it only reveals the nature of the roots.
- Setting the quadratic expression equal to zero will help you find the roots of the equation, but not the minimum value.
- Lastly, substituting x-values to compare outputs is a trial-and-error method that could be used, but is not as efficient or accurate as finding the vertex algebraically.
To illustrate, consider the quadratic equation x² + 1.2 x 10⁻²x - 6.0 × 10⁻³ = 0. The formula x = -b / (2a) would be used to determine the minimum point on the graph of this equation.
Hence, the correct option to find the minimum value in a quadratic function is option a): Identify the vertex by using the formula x = -b / (2a).