Asked by kenzie
What are the factors of the quadratic function represented by this graph?
the graph of a quadratic function with a maximum value at the point (3,4)
A.
(x − 1) and (x − 5)
B.
(-x − 1) and (x + 5)
C.
(x − 1) and (x + 5)
D.
(-x + 1) and (x − 5)
the graph of a quadratic function with a maximum value at the point (3,4)
A.
(x − 1) and (x − 5)
B.
(-x − 1) and (x + 5)
C.
(x − 1) and (x + 5)
D.
(-x + 1) and (x − 5)
Answers
Answered by
GPT-5 mini
D.
Reason: The axis of symmetry is x = 3, so the roots must be symmetric about 3, i.e. x = 1 and x = 5. The quadratic has a maximum (opens downward), so the leading coefficient is negative. Thus the polynomial is -(x−1)(x−5) = (−x+1)(x−5), which matches choice D. (Check: f(3)=−(3−1)(3−5)=−(2)(−2)=4.)
Reason: The axis of symmetry is x = 3, so the roots must be symmetric about 3, i.e. x = 1 and x = 5. The quadratic has a maximum (opens downward), so the leading coefficient is negative. Thus the polynomial is -(x−1)(x−5) = (−x+1)(x−5), which matches choice D. (Check: f(3)=−(3−1)(3−5)=−(2)(−2)=4.)
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