Graphing Quadratics Using Patterns (3.16.4) Flashcards
• To graph any function, follow these steps:
- Determine its basic shape centered at the origin.
- Determine its sign so you can sketch how it opens.
- Determine its steepness so you can sketch its shape.
- Determine its location according to any shift indicated.
• To graph any function, follow these steps:
- Determine its basic shape centered at the origin.
- Determine its sign so you can sketch how it opens.
- Determine its steepness so you can sketch its shape.
- Determine its location according to any shift indicated.
Your first step is to graph the general shape of the curve
centered at the origin.
In this example, only the x is squared, so you will have a
parabola as shown.
Your next step is to determine which direction the parabola will open. If the coefficient of the x-term is negative, the curve will open downward. Otherwise, it opens upward.
In this example, the coefficient is negative, so the curve opens downward, as shown.
The third step is to determine how wide or narrow the curve is; i.e., the curve’s steepness or pitch.
In this case, the x-term is multiplied by 3 which will make
the curve noticeably narrower than the generic parabola, as shown here.
Your final step is to check for any shifts of the vertex away from the origin.
In this example, the (x –1) indicates a move to the right 1
unit. The +2 indicates a move up 2 units.
You can see on the graph that the curve has moved its vertex to the right 1 and up 2.
Your first step is to graph the general shape of the curve
centered at the origin.
In this example, only the x is squared, so you will have a
parabola as shown.
Your next step is to determine which direction the parabola will open. If the coefficient of the x-term is negative, the curve will open downward. Otherwise, it opens upward.
In this example, the coefficient is negative, so the curve opens downward, as shown.
The third step is to determine how wide or narrow the curve is; i.e., the curve’s steepness or pitch.
In this case, the x-term is multiplied by 3 which will make
the curve noticeably narrower than the generic parabola, as shown here.
Your final step is to check for any shifts of the vertex away from the origin.
In this example, the (x –1) indicates a move to the right 1
unit. The +2 indicates a move up 2 units.
You can see on the graph that the curve has moved its vertex to the right 1 and up 2.
