Find the Vertex f(x)=3x^2-12x+1

Problem

ƒ(x)=3*x^2−12*x+1

Solution

1. Identify the coefficients of the quadratic function in the standard form ƒ(x)=a*x^2+b*x+c

a=3

b=−12

c=1

2. Apply the formula for the x-coordinate of the vertex, which is given by h=(−b)/(2*a)

h=(−(−12))/(2*(3))

h=12/6

h=2

3. Substitute the x-coordinate back into the original function to find the y-coordinate, k=ƒ(h)

k=3*(2)^2−12*(2)+1

k=3*(4)−24+1

k=12−24+1

k=−11

4. State the vertex as the ordered pair (h,k)

(h,k)=(2,−11)

Final Answer

Vertex=(2,−11)

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