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Turning Points for Quadratics

Turning Points for Quadratics

If the coefficient (the multiple) of the `x^2` term is positive, then the turning point is a minimum. If negative, the turning point is a maximum.

A quadratic curve is vertically symmetrical about its turning point, or vertex.

The `x`-value for the turning point is given by `-frac(b)(2a)` for a function `ax^2+bx+c`. Substituting this value into the equation gives the `y`-value.

Example 1

What are the coordinates for the turning point for the equation `y = -2x^2 - 4x + 6`?

The `x`-value is given by `-frac(b)(2a)` = `-frac(-4)(2 xx -2) = -1`.

Substituting `-2(-1)^2 - 4(-1) + 6 = -2 + 4 + 6 = 8`

Answer: (-1,8)

Example 2

Is the turning point a maximum or a minimum?

The coefficient for the squared term is negative, so the turning point is a maximum.

Graph of f(x)=-2x<sup>2-4x+6

Answer: A maximum.

See also Completing the Square