Question

The graph of a quadratic function increases through interval A, then decreases through interval B. If the vertex of thegraph is located at (5,9), which equation could represent this function?Interval A: -00 <3 < 5Interval B:5 << OOSelect one:O a. f() = (x + 5)2 + 9O b. f(x) = (x – 5)2 +9O c. f() = -(x + 5)2 +9O d. f(x) = -(x - 5)2 +9

Answer 1

The quadratic function with vertex (h,k) is

$y=(x-h)^2+k$

If the function is increases for interval,

$-\inftyand decreases for interval[tex]hThen the function opens in downward side and quadratic equation becomes,[tex]y=-(x-h)^2+k$

So quadratic equation with vertex (5,9) and increasing for interval,

$-\inftyand decrease through interval,[tex]5is,[tex]f(x)=-(x-5)^2+9$

Option D is correct.