Explain the Vertex Formula ?
The vertex formula is a convenient way of finding the vertex of the graph for any quadratic function. The graph of the quadratic equation f(x) = ax2 + bx + c has its vertex at:
(-b/2a, f(-b/2a))
In other words the x coordinate of the vertex is always x = -b/2a, which is also the equation for the axis of symmetry.
Symmetry
Note: this formula is derived from the standard form by completing the square.
Here's an example that you can look at:
Question: Use the vertex formula to find the vertex of the graph of the following function:
f(x) = -x 2 + 6x - 5
Solutions: Find the x-coordinate of the vertex first, using the vertex formula.
x = -b /2a
X = -6 / 2(-1)
X = -6/-2
X =3
This tells us that the vertex is the point (3, ?). We now need to find the y-coordinate, or functional value, for
x = 3.
f(3) = -(3) 2 + 6(3) - 5
= -9 + 18 -5
= 4
So, the vertex point of f(x) = -x2 +6x - 5 is the point (3,4)