Form a quadratic statement from the given:

Zeroes at 2 and 3, f(1)=12.

f(x)=?

a (x-2)(x-3) = 0

a[ x^2 -5x + 6 ] = 0

f(x) = a[ x^2 -5x + 6 ]
when x = 1
f(1) = 12 = a[ 1-5+6]
12 = 2 a
a = 6
so
f(x) = 6x^2 -30 x + 36

Well, since the zeros are at 2 and 3, we know that the factors of the quadratic equation are (x - 2) and (x - 3). So, the equation can be written as f(x) = a(x - 2)(x - 3), where 'a' is just a constant.

Now, we have f(1) = 12, which means when we substitute x = 1 in the equation, we should get 12. Let's do some math:

f(1) = a(1 - 2)(1 - 3) = a(-1)(-2) = 2a

So, we have 2a = 12. To solve for 'a', we simply divide both sides by 2: a = 6.

Plugging this value back into the equation, we have f(x) = 6(x - 2)(x - 3).

Voila!

To form a quadratic statement, we need to determine the quadratic equation in the form of f(x) = ax^2 + bx + c using the given information.

We know that the zeroes are at x = 2 and x = 3. From this, we can determine two factors of the quadratic equation, (x - 2) and (x - 3).

So, the quadratic equation can be written as follows:

f(x) = a(x - 2)(x - 3)

Now, we need to find the value of 'a'. We have the information that f(1) = 12. So we substitute x = 1 and f(x) = 12 into the equation:

12 = a(1 - 2)(1 - 3)
12 = a(-1)(-2)
12 = 2a

To solve for 'a', divide both sides of the equation by 2:

12/2 = a
6 = a

Now, we have the value of 'a'. Substitute it back into the quadratic equation:

f(x) = 6(x - 2)(x - 3)

Therefore, the quadratic statement is f(x) = 6(x - 2)(x - 3).

To form a quadratic statement, we need to use the fact that the given quadratic function has zeroes at 2 and 3.

When a quadratic function has zeroes at a and b, it can be written in factored form as (x - a)(x - b) = 0.

Therefore, the factored form of the quadratic function is (x - 2)(x - 3) = 0.

To find the expanded form of the quadratic function, we multiply the factors:

(x - 2)(x - 3) = x^2 - 2x - 3x + 6 = x^2 - 5x + 6

So, the quadratic function is f(x) = x^2 - 5x + 6.

Now, we need to find the value of f(1).

To find f(1), we substitute x = 1 into the quadratic function:

f(1) = (1)^2 - 5(1) + 6 = 1 - 5 + 6 = 2

Therefore, the quadratic statement is f(x) = x^2 - 5x + 6 and f(1) = 2.