Question

question 7 of 10
which describes the graph of $y = -(x + 6)^2 + 6$?

a. minimum at $(6, 6)$

b. minimum at $(-6, 6)$

c. maximum at $(6, 6)$

d. maximum at $(-6, 6)$

Explanation:

Step1: Recall the vertex form of a parabola

The vertex form of a parabola is \(y = a(x - h)^2 + k\), where \((h, k)\) is the vertex. If \(a>0\), the parabola opens upward (has a minimum), and if \(a<0\), it opens downward (has a maximum).

Step2: Identify \(a\), \(h\), and \(k\) from the given equation

For the equation \(y = -(x + 6)^2 + 6\), we can rewrite it as \(y=-1(x - (-6))^2+6\). So, \(a=-1\), \(h = - 6\), and \(k = 6\).

Step3: Determine if it's a maximum or minimum and the vertex

Since \(a=-1<0\), the parabola opens downward, so it has a maximum at the vertex \((h,k)=(-6,6)\).

Answer:

D. Maximum at \((-6, 6)\)