Graphing Key Features
Aligned to F-IF.C.7 — Common Core State Standards for Mathematics.
What this lesson teaches
To graph a function, plot its key features: intercepts (where it crosses the axes), and for a quadratic, its vertex. Then connect the points smoothly following the function's shape.
Worked examples
Example 1
Graph y = x^2 − 4. The y-intercept is (0, −4). Setting y = 0 gives x^2 = 4, so x = 2 or x = −2 — the x-intercepts are (2, 0) and (−2, 0), and the vertex is (0, −4).
Example 2
Graph y = |x| − 2: a V with its vertex at (0, −2) and x-intercepts at (−2, 0) and (2, 0).
Example 3
Intercepts, vertex and end behaviour are the features worth finding. Plotting random points rarely reveals any of them.
Practice questions
- Find the x- and y-intercepts of y = 2x − 6.
- Find the vertex and y-intercept of y = x^2 − 9.
- Where does the graph of y = x^2 touch 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
Graficar Características Clave
Para graficar una función, marca sus características clave: las intersecciones (donde corta los ejes) y, para una cuadrática, su vértice. Luego une los puntos suavemente siguiendo la forma de la función.
Ejemplo 1: Grafica y = x^2 − 4. La intersección con el eje y es (0, −4). Al hacer y = 0 queda x^2 = 4, así que x = 2 o x = −2: las intersecciones con el eje x son (2, 0) y (−2, 0), y el vértice es (0, −4).
Ejemplo 2: Grafica y = |x| − 2: una V con vértice en (0, −2) e intersecciones en (−2, 0) y (2, 0).
Ejemplo 3: Las intersecciones, el vértice y el comportamiento en los extremos son lo que vale la pena hallar. Graficar puntos al azar casi nunca revela ninguno.
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