Solve the vertex and axis of symmetry of the equation. Show your work and explain the steps you used to solve. f (x) = x2 − 6x + 4

Question

Solve the vertex and axis of symmetry of the equation. Show your work and explain the steps you used to solve.

f
(x) = x2 − 6x + 4

Answer 1

The graph of y = Ax²+Bx+C (A≠0) is a parabola.

 

  The x-coordinate of the vertex is -B/(2A).

 

So, for f(x) = x²-6x+4, the x-coordinate of the vertex is -(-6)/2 = 3

 

                                the y-coordinate of the vertex is f(3) = -5

 

       vertex = (3,-5) 

Answer 2

Recognize f(x) = x^2 - 6x + 4 = x^2-6x+9-5 = (x-3)^2 - 5. The vertex is (3,-5) (compare with standard form y = (x-h)^2 + k where vertex is (h,k))  and the axis of symmetry is x = 3.