Final answer:
To write a quadratic equation with zeros at 2 and 3 and a value of f(1) = 12, we can use the fact that the zeros of a quadratic equation are the x-intercepts of the corresponding quadratic function. The equation is -6(x - 2)(x - 3) = 0.
Step-by-step explanation:
To write a quadratic equation with zeros at 2 and 3 and a value of f(1) = 12, we can use the fact that the zeros of a quadratic equation are the x-intercepts of the corresponding quadratic function.
First, we know that the zeros are 2 and 3, so the factors of the equation are (x - 2) and (x - 3). Multiplying these factors together gives us (x - 2)(x - 3) = 0.
To find the value of the coefficient a, we can substitute the point (1, 12) into the equation. Plugging in x = 1 and y = 12, we get (1 - 2)(1 - 3) = a * 12. Simplifying this equation gives us -2a = 12, so a = -6.
Therefore, the quadratic equation with zeros at 2 and 3 and f(1) = 12 is -6(x - 2)(x - 3) = 0.