Can some one tell me how to find the vertex and create a "Quadratic function" in "Vertex form" from this table of value :
(-3,-0.5) (-2.5, -3) (-2, -4.5) (-1.5, -5) (-1, -4.5) -0.5, -3) and (0, -0.5)
These points look to be symmetric (compare the y-values for x = -3 and x = 0, or x = -2 and x = -1), so I don't think you're supposed to do a regression to create a "best fit" equation; I believe these points are exactly from
One method for finding the equation would be to plot the points and note, by symmetry, where the vertex must
be. Since the vertex
is the point (h, k), and since the vertex form of the equation is "y = a(x - h)2
+ k", you can plug the values for "h" and "k" into the equation.
They've given you seven points, only one of which was the vertex. Pick any of othe other points, and plug the x- and y-values into the above equation. Solve this for the value of "a".
Now that you have the values of "h", "k", and "a", you can fill in the vertex form of the equation to find your answer.
And after we have a vertex , determine whether it is a max or a min ?
If a quadratic is positive (that is, if its parabola opens upward), the vertex is the minimum; otherwise, the vertex is the maximum. (The lesson in the above link gives more information on this.)