If a equation is like this $-2(x+3)^2+25$ what is its turning point?

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Answer 1 · 2018-05-10T08:21:09

$color(blue)((-3 ,25)$

The turning point is the same as the vertex.

If we express a quadratic in the form:

$y=a(x-h)^2+k$

Then:

$bba$ is the coefficient of $x^2$ , $bbh$ is the axis of symmetry and $bbk$ is the maximum/minimum value of the function.

Also, if:

$a > 0$ then the parabola is of the form $uuu$

if:

$a < 0$ then the parabola is of the form $nnn$

The given function is in this form:

$h = -3$

$k=25$

Since $h$ is the axis of symmetry, this is the x coordinate of the vertex, and since $k$ is the max/min value it is the y coordinate of the vertex.

So:

$(h,k)->(-3,25)$

This is the vertex and hence the turning point of the function.

This can be seen on the graph:

enter image source here

If a equation is like this -2(x+3)^2+25-2(x+3)^2+25 what is its turning point?