Answer :
Answer:
To find a quadratic function in the form f(x) = ax^2 + bx + c with zeros at 3 and 2, we can use the fact that the zeros of a quadratic function are the values of x where the function equals zero.
If the function has zeros at 3 and 2, it means that when x = 3, the function equals zero, and when x = 2, the function also equals zero.
So, we can set up two equations:
1. When x = 3: 0 = a(3)^2 + b(3) + c
2. When x = 2: 0 = a(2)^2 + b(2) + c
Now, let's solve these equations to find the values of a, b, and c.
1. When x = 3: 0 = 9a + 3b + c
2. When x = 2: 0 = 4a + 2b + c
We have two equations with three variables, so we need one more equation to solve for all the variables. One way to do this is by using the fact that the coefficient of x^2 (a) is 2.
We can substitute the values of x and y from one of the given points into the equation and solve for the remaining variable. Let's use the point (3, 0):
0 = 9a + 3b + c
Substituting x = 3 and y = 0:
0 = 9a + 3b + c
0 = 9a + 3b + 0
0 = 9a + 3b
Now, we have three equations:
1. 0 = 9a + 3b + c
2. 0 = 4a + 2b + c
3. 0 = 9a + 3b
We can solve these equations simultaneously to find the values of a, b, and c. Let's solve them:
From equation 3, we can express b in terms of a:
b = -3a
Substituting this into equation 2:
0 = 4a + 2(-3a) + c
0 = 4a - 6a + c
0 = -2a + c
Now, we have two equations:
1. 0=9a+3b+c
2. 0.
