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How do you graph parabola given its vertex?
The vertex of a parabola doe not provide enough information to graph anything - other than the vertex!
What is the relationship of a vertex to a parabola?
The vertex is either the minimum (very bottom) or maximum (very top) of a parabola.
Does a parabola always have 2 x intercepts?
No, if the vertex of the parabola is (0, 0) it will only have one x intercept. The parabola might have zero x intercepts as well. For example: Y= x^2 + 1 would never touch the x line.
How are the vertices of the parabolas related to the equation of the quadratic function?
Suppose the equation of the parabola is y = ax2 + bx + c where a, b, and c are constants, and a ≠0. The roots of the parabola are given by x = [-b ± sqrt(D)]/2a where D is the discriminant. Rather than solve explicitly for the coordinates of the vertex, note that the vertical line through the vertex is an axis of symmetry for the parabola. The two roots are symmetrical about x = -b/2a so, whatever the value of D and whether or not the parabola has real roots, the x coordinate of the vertex is -b/2a. It is simplest to substitute this value for x in the equation of the parabola to find the y-coordinate of the vertex, which is c - b2/2a.
To find the value of a in a parabola opening left or right subtract the x value of the parabola at the vertex from the x value of the point on the parabola that is one unit the vertex?
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