15. Given information about the graph of a quadratic function, find its equation

Question

15. Given information about the graph of a quadratic function, find its equation Vertex (2,0) and point on graph (4,12) 16. Solve the following application problem. A rectangular field is to be enclosed by fencing. In addition to the enclosing fence, another fence is to divide the field into two parts, running parallel to two sides. If 1,200 feet of fencing is available, find the maximum area that can be enclosed 17. Find all zeros of the following polynomial functions, noting multiplicities fx)(x-3)(3x-1)(x-1)

Explanation / Answer

1) vertex = (2, 0 )

point = ( 4, 12 )

standard equation in vertex form is

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

plugging the values we get

12 = a ( 4 - 2)^2 + 0

12 = 4a

a = 3

hence , equation becomes

y = a ( 4 - 2)^2 + 0

y = 3 ( x - 2)^2

y = 3 (x^2 - 4x + 4 )

y = 3x^2 - 12x + 12

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