study guides for every class

that actually explain what's on your next test

Minimum value

from class:

Algebra and Trigonometry

Definition

The minimum value of a quadratic function is the lowest point on its graph, known as the vertex, when the parabola opens upwards. It represents the smallest y-value that the function attains.

congrats on reading the definition of minimum value. now let's actually learn it.

ok, let's learn stuff

5 Must Know Facts For Your Next Test

  1. For a quadratic function in standard form $f(x) = ax^2 + bx + c$ with $a > 0$, the minimum value occurs at $x = -\frac{b}{2a}$.
  2. The y-coordinate of the vertex gives the minimum value and can be found by evaluating $f(-\frac{b}{2a})$.
  3. A quadratic function has a minimum value if and only if its leading coefficient $a$ is positive.
  4. In vertex form $f(x) = a(x-h)^2 + k$, where $a > 0$, the minimum value is $k$ at $x = h$.
  5. The axis of symmetry of a quadratic function, given by $x = -\frac{b}{2a}$, passes through the vertex.

Review Questions

  • How do you determine whether a quadratic function has a minimum or maximum value?
  • What formula is used to find the x-coordinate of the vertex for a quadratic function in standard form?
  • If given a quadratic function in vertex form, how can you quickly identify its minimum value?
© 2024 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.
Glossary
Guides