Find the Vertex f(x)=-3x^2+6x-2

Problem

ƒ(x)=−3*x2+6*x−2

Solution

1. Identify the coefficients of the quadratic function in the standard form ƒ(x)=a*x2+b*x+c

a=−3

b=6

c=−2

2. Apply the formula for the xcoordinate of the vertex, which is h=(−b)/(2*a)

h=(−6)/(2*(−3))

3. Simplify the expression to find the value of h

h=(−6)/(−6)

h=1

4. Substitute the xcoordinate back into the original function to find the ycoordinate, k=ƒ(h)

k=−3*(1)2+6*(1)−2

5. Calculate the value of k

k=−3+6−2

k=1

Final Answer

Vertex=(1,1)

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