Equivalent Forms of a Function
Aligned to F-IF.C.8 — Common Core State Standards for Mathematics.
What this lesson teaches
Writing the same function in different forms reveals different properties. Standard form shows the y-intercept, factored form shows the zeros, and vertex form shows the maximum or minimum point.
Worked example
Take f(x) = x^2 − 6x + 5. Factored form (x − 1)(x − 5) shows zeros at x = 1 and x = 5. Vertex form, from completing the square, is (x − 3)^2 − 4, showing the minimum point (vertex) at (3, −4).
Practice questions
- Factor f(x) = x^2 − 4x − 5 to find its zeros.
- Write f(x) = x^2 + 2x + 1 in vertex form.
- What does the constant 7 reveal in f(x) = x^2 + 4x + 7?
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Formas Equivalentes de una Función
Escribir la misma función en formas distintas revela propiedades distintas. La forma estándar muestra la intersección con el eje y, la forma factorizada muestra los ceros, y la forma de vértice muestra el punto máximo o mínimo.
Ejemplo: Toma f(x) = x^2 − 6x + 5. La forma factorizada (x − 1)(x − 5) muestra ceros en x = 1 y x = 5. La forma de vértice, al completar el cuadrado, es (x − 3)^2 − 4, mostrando el punto mínimo (vértice) en (3, −4).
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