Final answer:
The function that represents a parabola with a vertex at (2,1) and a y-intercept at (0,3) is f(x) = 1/2(x - 2)² + 1.
The answer is option ⇒B
Step-by-step explanation:
To determine the function that represents a parabola with a vertex at (2,1) and a y-intercept at (0,3), we can use the standard form of a quadratic equation, which is:
f(x) = a(x - h)² + k
Where (h, k) represents the coordinates of the vertex.
In our case, the vertex is (2,1), so we have:
f(x) = a(x - 2)² + 1
To find the value of 'a', we can substitute the coordinates of the y-intercept (0,3) into the equation:
3 = a(0 - 2)² + 1
3 = 4a + 1
4a = 2
a = 1/2
Now, we can substitute the value of 'a' back into the equation to get the final function:
f(x) = 1/2(x - 2)² + 1
So, the correct function that represents the given parabola is f(x) = 1/2(x - 2)² + 1.
The answer is option ⇒B
Your question is incomplete, but most probably the full question was:
Select the function that represents a parabola with a vertex at (2,1) and y-intercept (0,3).
- A) f(x) = 2(x + 2)² + 1
- B) f(x) = 1/2(x - 2)² + 1
- C) f(x) = 2(x - 2)² + 1
- D) f(x) = 7/2(x + 2) + 1