Vertex form equation of a parabola :
y = a(x - h)2 + k
Characteristics of graph :
The vertex is (h, k).
The axis of symmetry is x = h.
The graph opens up if a > 0 and opens down if a < 0.
Example 1 :
Graph : y = -½(x + 3)2 + 4
Solution :
Equation of the parabola is in vertex form :
y = a(x - h)2 + k
a = -½, h = -3, and k = 4
Because a < 0, the parabola opens down.
To graph the function, first plot the vertex (h, k) = (-3, 4).
Draw the axis of symmetry x = -3.
Plot two points on one side of it, such as (-1, 2) and (1, -4). Use symmetry to plot two more points, such as (-5, 2) and (-7, -4).
Use symmetry to complete the graph.
Example 2 :
Graph : y = (x - 3)2 + 2
Solution :
Equation of the parabola is in vertex form :
y = a(x - h)2 + k
a = 1, h = 3, and k = 2
Because a < 0, the parabola opens down.
To graph the function, first plot the vertex (h, k) = (3, 2).
Draw the axis of symmetry x = 3
Plot two points on one side of it, such as (1, 3) and (1, 6). Use symmetry to plot two more points, such as (4, 3) and (5, 6).
Use symmetry to complete the graph.
Example 3 :
Graph : y = -(x - 3)2 + 2
Solution :
Equation of the parabola is in vertex form :
y = a(x - h)2 + k
a = -1, h = 3, and k = 2
Because a < 0, the parabola opens down.
To graph the function, first plot the vertex (h, k) = (3, 2).
Draw the axis of symmetry x = 3.
Plot two points on one side of it, such as (2, 1) and (1, -2). Use symmetry to plot two more points, such as (4, 1) and (5, -2).
Use symmetry to complete the graph.
Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
©All rights reserved. onlinemath4all.com
May 17, 24 08:12 AM
May 14, 24 08:53 AM
May 14, 24 02:48 AM