MATH SOLVE

3 months ago

Q:
# Complete the square to determine the maximum or minimum value of the function defined by the expression.−x^2 − 6x + 6A) minimum value at 3 B) maximum value at 15 C) minimum value at −1 D) minimum value at −6

Accepted Solution

A:

Answer:maximum of 15Step-by-step explanation:Complete the square on y = -x² - 6x + 6First, factor out -1 from the first 2 terms so the x² term is positive y = -(x² + 6x) + 6A quadratic equation is in the form of y = ax² + bx + c. To complete the square, take half of the b term (here, the b term is 6), then square it...6/2 = 33² = 9Now add and subtract that from the equation...y = -(x² - 6x + 9 - 9) + 6Now pull out the -9 from the parenthesis, be careful though, there is a -1 multiplier in front of the parenthesis, so it come out as a positive 9y = -(x² - 6x + 9) + 9 + 6 x² - 6x + 9 is a perfect square (we did this by completing the square), so it factors to (x - 3)², 9 + 6 = 15, so our equation becomes...y = -(x - 3)² + 15This is now in vertex form, which is either the minimum or maximum.Vertex form is y = a(x - h)² + k, where (h, k) is the vertex. If a > 0, then the vertex is a minimum, if a < 0, then the vertex is a maximum.We have a vertex of (3, 15) which is a maximum since a < 0. The maximum value is the y coordinate, which is 15The x coordinate is positive 3 because we have (x - h)² and h is 3 in this case