How do I figure out?How do I figure out whether or not the vertex of y=-2(x-2)^2-2 is a minimum value?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

To determine if the vertex of y=-2(x-2)^2-2 is a negative value or a positive one, we find the second derivative of y and see if it is positive or negative. If the second derivative at the vertex if positive it is a minimum value, else it is a maximum value.

y = -2*x^2 - 2

=> y' = -4x

=> y'' = -4

This gives that the value at the vertex is a maximum.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We know that if leading coefficient of the quadratic is positive, than the parabola has a minimum point, this one being the vertex of the parabola.

y=ax^2+bx+c

a is the leading coefficient

If the leading coefficient is negative, than the vertex represents a maximum point.

We can notice that the leading coefficient is negative, a=-2, so the parabola has a maximum point.

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