Maximum value

Definition

The maximum value of a quadratic function refers to the highest point on its graph, which occurs at its vertex if the parabola opens downward. It is relevant when the leading coefficient of the quadratic term is negative.

5 Must Know Facts For Your Next Test

1. The maximum value occurs at the vertex of the parabola when it opens downward.
2. For a quadratic function $f(x) = ax^2 + bx + c$ with $a < 0$, the maximum value is given by $f(-\frac{b}{2a})$.
3. The x-coordinate of the vertex can be found using $-\frac{b}{2a}$.
4. The y-coordinate of the vertex, which gives the maximum value, can be calculated by substituting $x = -\frac{b}{2a}$ back into the function.
5. The graph of a quadratic function that has a maximum value is a parabola that opens downward.

Review Questions

• What condition must be true for a quadratic function to have a maximum value?
• How do you find the x-coordinate of the vertex for a quadratic function?
• How can you determine if a quadratic function's graph will open upwards or downwards?

Related terms

Vertex: The point where the parabola changes direction, representing either a maximum or minimum value.

Axis of Symmetry: A vertical line passing through the vertex of a parabola, given by $x = -\frac{b}{2a}$ for a quadratic function $ax^2 + bx + c$.

Leading Coefficient: The coefficient 'a' in front of $x^2$ in a quadratic equation $ax^2 + bx + c$, determining whether the parabola opens upwards or downwards.