SOLUTION: The graph of a quadratic function (a parabola) has x -intercepts 1 and -3 and a range consisting of all numbers less than or equal to 4. Determine an expression for the function.

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: The graph of a quadratic function (a parabola) has x -intercepts 1 and -3 and a range consisting of all numbers less than or equal to 4. Determine an expression for the function.       Log On


   



Question 769789: The graph of a quadratic function (a parabola) has x -intercepts 1 and -3 and a
range consisting of all numbers less than or equal to 4. Determine an expression for the function.

Answer by reviewermath(1029) About Me  (Show Source):
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Q:
The graph of a quadratic function (a parabola) has x -intercepts 1 and -3 and a
range consisting of all numbers less than or equal to 4. Determine an expression for the function.
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A:
y = a(x - 1)(x + 3)
y = a%28x%5E2+%2B+2x+-+3%29
y = ax%5E2+%2B+2ax+-+3a
In y = Ax%5E2+%2B+Bx+%2B+C the vertex is (h,k) where h = %28-B%29%2F2A and k = %284AC+-+B%5E2%29%2F4A.
If A < 0, then y ≤ k.
In y = ax%5E2+%2B+2ax+-+3a,
k = %284a%28-3a%29+-+%282a%29%5E2%29%2F4a = -4a
-4a = 4
a = -1
so the quadratic function is
highlight%28y+=+-x%5E2+-+2x+%2B+3%29.