Write the quadratic function from the table of values

[honest_denverco09]

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)

And after we have a vertex , determine whether it is a max or a min ?

Thanks!

[stapel_eliz]

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 an equation.

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.)

[honest_denverco09]

Thank you for your answering!

I got the second part (Whether the vertex is max or min), but i still be stuck in part that how can i figure out the coordinates of the vertex in these seven points, will the vertex be the middle point ? If so, how can i find the vertex when the number of points that are given is the even numbers ?

Also can i find the vertex of quadratic function by using the way that is used to find the slope of linear function "slope = (y1 - y2)/(x1-x2)" ?
Thanks

[stapel_eliz]

i still be stuck in part that how can i figure out the coordinates of the vertex in these seven points, will the vertex be the middle point ? If so, how can i find the vertex when the number of points that are given is the even numbers ?

It's not so much a matter of "even" or "odd", as much as symmetry. You could have four points for a quadratic (say, (-4, 0), (-3, -1), (-1, -1), and (0, 0)), and all you would need to do, for finding the vertex, would be to note the symmetry (in this example, the fact that x = -4 and x = 0 have the same y-value, and x = -3 and x = -1 share another y-value); the vertex would be at the point directly between (in this example, at x = -2).

Also can i find the vertex of quadratic function by using the way that is used to find the slope of linear function "slope = (y1 - y2)/(x1-x2)" ?

Since a quadratic does not have a constant slope, no, the slope formula would not apply. Sorry!

[honest_denverco09]

Thank you for your answering!