Write the function f(x) = 3x^2 - 12x + 61 in vertex form.
A) f(x) = 3(x - 2)^2 + 49
B) f(x) = 3(x + 2)^2 + 49
C) f(x) = 3(x - 2)^2 + 61
D) f(x) = 3(x + 2)^2 + 61

Question

Write the function f(x) = 3x^2 - 12x + 61 in vertex form. A) f(x) = 3(x - 2)^2 + 49 B) f(x) = 3(x + 2)^2 + 49 C) f(x) = 3(x - 2)^2 + 61 D) f(x) = 3(x + 2)^2 + 61

SnapAndSolve AI · Accepted Answer

The vertex form of a quadratic function is given by f(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

To convert f(x) = 3x^2 - 12x + 61 to vertex form, we complete the square:

Factor out the 3 from the x terms: f(x) = 3(x^2 - 4x) + 61
Complete the square inside the parentheses: x^2 - 4x becomes (x - 2)^2 - 4
Adjust the equation: f(x) = 3((x - 2)^2 - 4) + 61
Simplify: f(x) = 3(x - 2)^2 - 12 + 61
Final vertex form: f(x) = 3(x - 2)^2 + 49

The correct answer is A) f(x) = 3(x - 2)^2 + 49.

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Write the function f(x) = 3x^2 - 12x + 61 in vertex form. A) f(x) = 3(x - 2)^2 + 49 B) f(x) = 3(x + 2)^2 +...

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