+63 Give an example of a quadratic function that has zeroes at x=2and 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.
+2653 We know that a quadratic function with roots at x=2 and x=4 can be written in the factored form as:
a(x−2)(x−4)
We are also given that the function takes the value 6 when x=3. This translates to the equation: a(3−2)(3−4)=6 which simplifies to −a=6
Since we already know that a cannot be 0 (the function wouldn't be quadratic), we can divide both sides by −1 to get a=−6
Plugging this value of a back into the factored form, we get the quadratic function: −6(x−2)(x−4)
Expanding this expression, we get the answer in the desired form: −6x^2 + 36x + 48
So the answer is -6x^2 + 36x + 48.
