Answer:
Part 1) [tex]f(x)=(x-2)^{2}-16[/tex]
Part 2) The function's correct axis of symmetry is x=2
Option f(x) = (x - 2)² - 16, x = 2
Step-by-step explanation:
we have
[tex]f(x)=x^{2} -4x-12[/tex]
This is a vertical parabola open upward
The vertex is the minimum
Part 1) Convert to vertex form
Complete the square. Remember to balance the equation by adding the same constants to each side.
[tex]f(x)=(x^{2} -4x+2^2)-12-2^2[/tex]
[tex]f(x)=(x^{2} -4x+4)-16[/tex]
Rewrite as perfect squares
[tex]f(x)=(x-2)^{2}-16[/tex] ----> function in vertex form
Te vertex is the point (2,-16)
Part 2) Find the axis of symmetry
we know that
The equation of the axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex
The vertex is the point (2,-16)
therefore
The function's correct axis of symmetry is x=2
