what is the y - value of the vertex of the function f(x)=-(x + 8)(x - 14)?\n3\n6\n112\n121

Explanation:

Step1: Expand the function

[ \begin{align*} f(x)&=-(x + 8)(x - 14)\ &=-(x^{2}-14x+8x - 112)\ &=-(x^{2}-6x - 112)\ &=-x^{2}+6x + 112 \end{align*} ]

Step2: Find the x - coordinate of the vertex

For a quadratic function (y = ax^{2}+bx + c), the x - coordinate of the vertex is (x=-\frac{b}{2a}). Here (a=-1), (b = 6), so (x=-\frac{6}{2\times(-1)} = 3).

Step3: Find the y - coordinate of the vertex

Substitute (x = 3) into the function (f(x)=-x^{2}+6x + 112). Then (f(3)=-3^{2}+6\times3 + 112=-9 + 18+112=121).

Answer:

121