Maximun and minimum value of a function?

 y = 2(x + 2)² – 3 ... FYI: This is in the vertex form of a parabola (or quadratic)

It can be seen that the first term: 2(x + 2)²  CANNOT be negative, so it has a

minimum value of zero at (x  =  - 2) ....... and the minimum y_value = - 3

The maximum y_value = +∞ , at either:  x = +∞  OR  x = - ∞

based on the first term.

The minimum value at the vertex is an Absolute Minimum: (x, y) = (- 2, - 3)

For any quadratic, write it indoors the variety f(x) = a x² + b x + c, the area a, b, & c are any actual numbers. Then the line of symmetry would desire to be x = -b / (2a). consequently f(x) = -x² + 6 might have the line of symmetry at x = 0 / (-2) = 0, the y-axis. So x = 0. the utmost value for this social amassing is that if fact be counseled (0,6). Subtitute x = 0 into the equation f (0) - 6- 0 = 0. How do i are conscious of this is a optimal value? i'm happy you asked! The study in front of the x² term shows wherein course the graph faces. no count kind quantity no count if this is useful, the graph is concave up, unfavorable the concave down.