Maximum value

Definition

The maximum value of a quadratic function is the highest point on its graph, which occurs at the vertex when the parabola opens downwards. It is the largest y-value that the function can attain.

5 Must Know Facts For Your Next Test

1. The maximum value of a quadratic function $f(x) = ax^2 + bx + c$ occurs at the vertex if $a < 0$.
2. The x-coordinate of the vertex is given by $x = -\frac{b}{2a}$.
3. The y-coordinate (maximum value) at the vertex can be found by substituting $x = -\frac{b}{2a}$ back into the function.
4. A quadratic function will have a maximum value only if its leading coefficient (a) is negative.
5. The maximum value represents the peak point of a downward-opening parabola.

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 in a quadratic function?
• Explain how to determine the maximum value of $f(x) = -3x^2 + 6x - 5$.

Related terms

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

Parabola: A symmetric curve formed by quadratic functions, which can open upwards or downwards.

Axis of Symmetry: A vertical line that divides a parabola into two symmetric halves, passing through its vertex and given by $x = -\frac{b}{2a}$.