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The turning point which is the change from an increasing to decreasing interval or vice-versa. It is a point so it is written as a coordinate pair (x,y). If the point is at the bottom of the function, it is called a minimum. If the point is at the top of the function, it is called a maximum.

For quadratics: If a quadratic is written in standard form, rewriting it in vertex form will provide the coordinates for the vertex. vertex form

Once it's written in vertex form, the number in with the x is the x coordinate of the vertex BUT OPPOSITE SIGN. The number outside the parentheses is the y coordinate just the way it is. The vertex is ( -3,-14).

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Vertex/Turning points from graph using Ti-84:

Same quadratic Example: Put the equation on the calculator using y= button.

equation on ti

Use graph button and ZOOM in or out until you can see the vertex.

graph on ti

Decide if it's a maximum(at the top) or minimum(at the bottom). Use the CALC button and select maximum or minimum and press enter.

CALC screen

Use the arrow keys to mark the left side and hit ENTER and right side of the vertex and hit ENTER and then ENTER when it says GUESS to see the answer at the bottom of the screen. If there's a bunch of zeros or nines after the decimal place, round it to the nearest integer.

vertex solution

The vertex is (-3,-14).