How do you find the maximum value of # Y= -2(x+5)²-8#?

Question

Aurora Alvarado · Accepted Answer

The maximum value of the function is #-8#.

This quadratic function is in vertex form, which is #y = a(x - h)^2 + k#, where #(h, k)# is the vertex of the graph of the function. Also, if #a >0#, the parabola will open upward and the #y#-coordinate of the vertex will be the minimum value of the curve. If #a <0#, the parabola will open downward and the #y#-coordinate of the vertex will be the maximum value of the curve. In #y = -2(x + 5)^2 - 8#, #a = -2# and #-2 < 0#, so the parabola will open downward and the maximum value of the curve will be the #y#-coordinate of the vertex, or #k#. In this equation, #k = -8#, so the maximum valu of the function is #-8#.

Emilia Aguilar · Answer

undefined To find the maximum value of the function $ Y = -2(x + 5)^2 - 8 $, you can follow these steps:

1. Recognize that the given function is a quadratic function in the form $ Y = a(x - h)^2 + k $, where $ a $ is the coefficient of the squared term, and $ (h, k) $ represents the coordinates of the vertex of the parabola.

2. In the given function, $ a = -2 $, $ h = -5 $, and $ k = -8 $.

3. The vertex of the parabola is at the point $ (h, k) = (-5, -8) $.

4. Since the coefficient of the squared term $ a = -2 $ is negative, the parabola opens downwards. Therefore, the vertex represents the maximum point of the function.

5. Therefore, the maximum value of the function $ Y $ occurs at the vertex $ (-5, -8) $, and the maximum value of $ Y $ is $ -8 $.