Answer:
- f(x) = 3(x - 3)^2 - 3
Step-by-step explanation:
<u>Let the base function be</u>
- f(x) = ax^2
<u>It has the vertex at (3, -3), so it is translated 3 units right and 3 units down:</u>
- f(x) = a(x - 3)^2 - 3
It has zero's at (2, 0) and (4, 0)
<u>Substitute and solve for a:</u>
- a(x - 3)^2 - 3 = 0
- a(2 - 3)^2 = 3
- a = 3
or
- a(4 - 3)^2 - 3 = 0
- a = 3
<u>So the function is:</u>
- f(x) = 3(x - 3)^2 - 3
<em>See the attached</em>
