GRAFICAR FUNCIONES CUADRÁTICAS Super facil
How to Graph a Quadratic Function
Introduction to Cartesian Plane
- Daniel Carreón introduces the topic of graphing quadratic functions and emphasizes the importance of understanding basic concepts.
- The Cartesian plane consists of two intersecting number lines: the horizontal axis (x-axis, blue) and the vertical axis (y-axis, green), which meet at the origin.
Understanding Quadratic Equations
- A quadratic equation is defined as one where x is raised to the second power, resulting in a parabolic graph.
- The standard form of a quadratic equation is ax^2 + bx + c , where:
- a : coefficient of x^2
- b : coefficient of x
- c : constant term
Identifying Coefficients
- For the example equation y = x^2 - 6x + 9 :
- a = 1
- b = -6
- c = 9
Finding the Vertex
- The vertex can be calculated using the formula:
[ x = -b/2a ]
Substituting values gives:
[ x = --6/2(1) = 3 ]
- This indicates that the vertex lies on the x-axis at point (3, y).
Calculating y-values for Vertex
- To find y when x = 3 :
[ y = (3)^2 - 6(3) + 9 = 0 ]
Thus, vertex coordinates are (3,0).
Completing Values for Graphing
- Two values before and after the vertex are chosen:
- Before: x = 1, 2
- After: x = 4,5
Calculating Additional Points
- For x = 1:
- Calculation yields:
[ y = (1)^2 -6(1)+9 =4] → Point (1,4).
- For x = 2:
- Calculation yields:
[ y =(2)^2 -6(2)+9 =1] → Point (2,1).
- For x = 4:
- Calculation yields:
[ y =(4)^2 -6(4)+9 =1] → Point (4,1).
- For x =5:
- Calculation yields:
[ y =(5)^2 –6(5)+9=4] → Point (5,4).
How to Graph Points on a Cartesian Plane
Introduction to Graphing Points
- The speaker begins by discussing the process of graphing points on a Cartesian plane, emphasizing the importance of understanding how to locate and plot coordinates accurately.
- A recommendation is made for viewers unfamiliar with graphing to watch an earlier video focused specifically on the Cartesian plane.
Step-by-Step Point Plotting
First Point: (1, 4)
- The first point discussed is (1, 4). The speaker explains how to find this point by locating '1' on the x-axis and '4' on the y-axis.
- After identifying these values, lines are drawn until they intersect at the plotted point (1, 4).
Second Point: (2, 1)
- Next, the speaker plots the second point (2, 1), guiding viewers through finding '2' on the x-axis and '1' on the y-axis.
- Lines are again drawn from these coordinates until they meet at point (2, 1).
Third Point: (3, 0)
- The third coordinate discussed is (3, 0). The speaker locates '3' on the x-axis and '0' on the y-axis.
- This results in plotting point (3, 0), which serves as a vertex in this context.
Fourth Point: (4, 1)
- Moving forward to point (4, 1), where '4' is found along the x-axis and '1' along the y-axis.
- As before, lines are drawn until they intersect at this new coordinate.
Fifth Point: (5, 4)
- Finally, for point (5, 4), viewers learn to locate '5' on the x-axis and '4' again on the y-axis.
- Once all points are plotted—(1, 4), (2, 1), (3, 0), (4, 1), and (5, 4)—the speaker notes that connecting them reveals a positive parabola.
Conclusion