For the function f(x) = 3x^2 - 12x + 9, find the vertex. (2021)

For the function f(x) = 3x^2 - 12x + 9, find the vertex. (2021)

Step 1: Identify the coefficients a, b, and c from the function f(x) = 3x^2 - 12x + 9. Here, a = 3, b = -12, and c = 9.
Step 2: Use the formula for the x-coordinate of the vertex, which is x = -b/(2a).
Step 3: Substitute the values of b and a into the formula: x = -(-12)/(2*3).
Step 4: Simplify the expression: x = 12/(6) = 2.
Step 5: Now, find the y-coordinate of the vertex by substituting x = 2 back into the function f(x).
Step 6: Calculate f(2): f(2) = 3(2^2) - 12(2) + 9.
Step 7: Simplify f(2): f(2) = 3(4) - 24 + 9 = 12 - 24 + 9 = -3.
Step 8: The vertex of the function is at the point (2, -3).

Quadratic Functions – Understanding the standard form of a quadratic function and how to find its vertex using the formula x = -b/(2a).
Vertex Calculation – Calculating the vertex of a parabola by substituting the x-coordinate back into the function to find the corresponding y-coordinate.