If the graph of f (x)=ax2+bx+c then how do we know the value of b from the graph. We will come to know the value of a & c by the shape of the graph like open upward or downward but what about 'b' explain
http://jwilson.coe.uga.edu/EMAT6680Su08/Henderson/Assignment3.html
Notice how the vertex shifts, and the parabola opens.
To determine the value of b from the graph of the quadratic function f(x) = ax^2 + bx + c, we need to understand the role of b in shaping the graph.
The coefficient b affects the symmetry and position of the graph. Specifically, b determines the x-coordinate of the vertex of the parabola, which is the point where the graph reaches its minimum or maximum.
To find the value of b from the graph, follow these steps:
1. Identify the vertex of the parabola. The vertex is the lowest point of the graph for an upward facing (a > 0) parabola, or the highest point for a downward facing (a < 0) parabola.
2. Once you have the coordinates of the vertex (h, k), where h is the x-coordinate and k is the y-coordinate, substitute these values into the equation f(x) = ax^2 + bx + c to form an equation involving only b.
For example, if the vertex is (3, 5), we substitute these values into the equation: 5 = a(3)^2 + b(3) + c.
3. If you have additional information, such as the coordinates of another point on the graph, you can further substitute those values into the equation to form another equation involving b.
4. Solve the resulting equations simultaneously to find the value of b.
It's important to note that if you only have the graph and not any other points, it may not be possible to determine the exact value of b. However, you can make reasonable estimates by visually analyzing the symmetry of the parabola and the approximate position of the vertex.