Parabolas An equation in two variables where one of the variables has a degree of
two and the other variable has a degree of one will form a . After finding this
single point, all other points will either be above or below the vertex
depending on the sign of the squared variable term. If the second
degree variable term has a positive coefficient all points will be above
the vertex. If the second degree variable term has a negative coefficient all
points will be below the vertex. For example, vertex_{
}, would be a parabola that would rise from the
vertex. On the otherhand, _{
}, would be a parabola that would fall from the
vertex. First you must determine the vertex. The vertex may be found by
first finding the x-value of the point which is _{
}.
*Note: the a and b are identified by the coefficients of the quadratic
function when written in the standard form ..._{}Once you find the x-value, plug that value back into
the equation and calculate the corresponding y-value. For the parabola
One way to find other points on the parabola is to find the x-intercepts and y-intercept. You may be able to factor the polynomial and use the zero factor property to determine x-intercepts. To determine the y-intercept, let x = 0 and calculate the y-value. It may be helpful to review solving second quadratic equations. Another way to find other pairs
of points could be to choose two arbitrary values for x on one side of the
vertex and calculate the corresponding
y-values. Once you have found these points, you can reflect those
points onto the opposite side of the vertex. For example, using the same
equation where we just found the vertex, suppose we choose x = 1 and x =
0 to be two values for x to the right of the vertex. Then The views and
opinions expressed in this page are strictly those of Mary Lou Baker. This page was edited on 15-Nov-2007 |