Give an example of a quadratic function that has zeroes at $x=2$ and $x=4$, and that takes the value $6$ when $x=3$. Enter your answer in the expanded form "ax^2 + bx + c", where a,b,c are replaced by appropriate numbers.
Since it has zeroes at x=2 and x=4, the quadratic can be written in the form y=a(x−2)(x−4). You can substitute the point (3,6) to get that 6=a(3−2)(3−4), so a=−6. Thus, we get the answer of −6(x−2)(x−4)=−6(x2−6x+8)=−6x2+36x−48.
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