using formula v=-b/2a, 4ac-b^2/4a
graph the quadratic function f(x)=x^2-6x+5
To graph the quadratic function f(x) = x^2 - 6x + 5 using the given formula v = -b/2a and 4ac - b^2/4a, we need to find the vertex (v) and the axis of symmetry.
1. Find the vertex (v):
The vertex formula is v = -b/2a. In this case, a = 1, b = -6.
v = -(-6) / (2 * 1)
v = 6 / 2
v = 3
So, the vertex of the quadratic function is (3, f(3)).
2. Find the axis of symmetry:
The axis of symmetry is a vertical line passing through the vertex. The equation for the axis of symmetry is x = v. Therefore, the axis of symmetry for this quadratic function is x = 3.
Now, let's plot the graph:
1. Plot the vertex, which we found to be (3, f(3)):
Mark a point at (3, f(3)), which is (3, (3)^2 - 6(3) + 5), simplify to (3, -1).
2. Find additional points:
To find other points on the graph, plug in different values for x into the quadratic function and calculate the corresponding y-values.
For instance, let's choose x = 0:
f(0) = (0)^2 - 6(0) + 5
f(0) = 0 - 0 + 5
f(0) = 5
So, we have another point (0, 5).
Similarly, let's choose x = 6:
f(6) = (6)^2 - 6(6) + 5
f(6) = 36 - 36 + 5
f(6) = 5
So, we have another point (6, 5).
3. Plot the points:
Plot the points (3, -1), (0, 5), and (6, 5) on the graph.
4. Draw the parabolic curve:
Using the points plotted, draw a smooth curve that passes through all the points.
The resulting graph will be a downward-opening parabola with the vertex at (3, -1) and the axis of symmetry at x = 3.