Revealing Properties by Rewriting
Aligned to F-IF.C.8 — Common Core State Standards for Mathematics.
What this lesson teaches
Writing a quadratic in factored form reveals its zeros, while vertex form reveals its maximum or minimum. Choose the form that shows the property you want.
Worked examples
Example 1
Rewrite y = x^2 − 6x + 8 in factored form to find its zeros. It factors as (x − 2)(x − 4), so the zeros are x = 2 and x = 4.
Example 2
y = 2(x − 3)² + 1 shows the vertex (3, 1) at a glance and shows that y is never below 1.
Example 3
Rewriting never changes the function, only what is easy to see. All three forms graph the same curve.
Practice questions
- Factor y = x^2 + 5x + 6 and state its zeros.
- Factor y = x^2 − 16 and state its zeros.
- The form y = (x − 3)^2 + 1 shows a minimum. Give the vertex.
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
Revelar Propiedades al Reescribir
Escribir una cuadrática en forma factorizada revela sus ceros, mientras que la forma de vértice revela su máximo o mínimo. Elige la forma que muestre la propiedad que buscas.
Ejemplo 1: Reescribe y = x^2 − 6x + 8 en forma factorizada para hallar sus ceros. Se factoriza como (x − 2)(x − 4), así que los ceros son x = 2 y x = 4.
Ejemplo 2: y = 2(x − 3)² + 1 muestra el vértice (3, 1) de un vistazo y muestra que y nunca baja de 1.
Ejemplo 3: Reescribir nunca cambia la función, solo lo que es fácil de ver. Las tres formas grafican la misma curva.
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