Vertex and Intercepts od a Quadratic Graph
Vertex
The quadratic equation has an extreme value located at the vertex of the graph. This vertex point is either the highest point on the graph of the equation or the lowest point:
Finding the vertex of a parabola without graphing
The location of the coordinates of the vertex of the graph of y=ax^{2}+bx+c depends only on the coefficients of a and b:
Coordinates of the vertex: (the yvalue is found by substituting the xvalue)
Find the vertex of f(x)=x ^{2}+6x+8
1. Find the xcoordinate of the vertex by using the formula , where a=1 and b=6:
2. Find the ycoordinate of the vertex by evaluating f(3)
f(3)=(3)^{2}+6(3)+8=918+8=1
Hence, the vertex is at (3,1)
Intercepts
The intercepts of a parabola are where the curve or graph of the function crosses the axis.
Finding the intercepts of a parabola without graphing.

To solve for the xintercepts of a quadratic function, you set f(x) equal to 0 (this is the same as setting y equal to 0)and then solve for x.
 To solve for the yintercept of a quadratic function, you set x equal to 0 and solve for f(x). A function has only one yintercept.
Find the xintercept(s) and the yintercept(s) of the quadratic equation y=x^{2}4
Step 1. First, find the yintercept. Since the yintercept is the point where the graph crosses the yaxis, the value for x at this point is zero. Because we know that x=0, plug 0 in for x in the equation and solve for x.
y=x^{2}4
y=0^{2}4
y=04
y=4
Therefore, the yintercept is (0,4)
Step 2. Next, find the xintercept(s). The xintercept is the point, or points in this case, where the graph crosses the xaxis. In this case, we plug 0 in for y because y is always zero along the xaxis. Solve for x.
y=x^{2}4
0=x^{2}4
0+4=x^{2}4+4
4=x^{2}
So x=2 and x=2
The xintercepts are (2,0) and (2,0)
Step 3. To verify that the intercepts are correct, graph the equation on the coordinate plane:
