Zeros of Polynomials and Their Graphs
Aligned to A-APR.B.3 — Common Core State Standards for Mathematics.
What this lesson teaches
When a polynomial is factored, each factor (x − r) gives a zero at x = r, where the graph crosses or touches the x-axis. Plotting the zeros along with the end behavior gives a rough sketch.
Worked example
For p(x) = (x + 1)(x − 2)(x − 3), the zeros are x = −1, 2, and 3. This cubic rises to the right, so the graph crosses the x-axis at each of those three points.
Practice questions
- Find the zeros of p(x) = (x − 4)(x + 5).
- Find the zeros of p(x) = x(x − 2)(x + 3).
- For p(x) = (x − 1)^2(x + 2), state where the graph touches versus crosses the x-axis.
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
Ceros de polinomios y sus gráficas
Cuando un polinomio está factorizado, cada factor (x − r) da un cero en x = r, donde la gráfica cruza o toca el eje x. Marcar los ceros junto con el comportamiento en los extremos da un bosquejo aproximado.
Ejemplo: Para p(x) = (x + 1)(x − 2)(x − 3), los ceros son x = −1, 2 y 3. Esta cúbica sube hacia la derecha, así que la gráfica cruza el eje x en cada uno de esos tres puntos.
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