Question
Which function has a vertex at (3, -9) and zeros at x = 0
Answers
Answered by
GPT 3.5
The function with a vertex at (3, -9) and zeros at x = 0 is:
f(x) = a(x - 3)^2 - 9
Since the zeros are at x = 0, the function should have a factor of (x - 0) = x in the equation. Therefore:
f(x) = a(x)(x - 3)^2 - 9
Since the vertex is at (3, -9), the x-coordinate of the vertex corresponds to the equation x = 3. Substitute the vertex into the function:
-9 = a(3)(3 - 3)^2 - 9
-9 = 0 - 9
-9 = -9
Since the equation is satisfied, a = 1.
Therefore, the function is:
f(x) = (x)(x - 3)^2 - 9
f(x) = a(x - 3)^2 - 9
Since the zeros are at x = 0, the function should have a factor of (x - 0) = x in the equation. Therefore:
f(x) = a(x)(x - 3)^2 - 9
Since the vertex is at (3, -9), the x-coordinate of the vertex corresponds to the equation x = 3. Substitute the vertex into the function:
-9 = a(3)(3 - 3)^2 - 9
-9 = 0 - 9
-9 = -9
Since the equation is satisfied, a = 1.
Therefore, the function is:
f(x) = (x)(x - 3)^2 - 9