Answer:
Part 1) Option A. The axis of symmetry is x=4
Part 2) Option C. minimum
Part 3) Option A. (4,-4)
Part 4) Option B. (2,0) and (6,0)
Step-by-step explanation:
we have
[tex]f(x)=x^{2}-8x+12[/tex]
Part 1) What is the axis of symmetry of the parabola described by the equation above?
we know that
The equation above is a vertical parabola open upward
The axis of symmetry is the x-coordinate of the vertex
Find the vertex of the parabola (convert the equation in vertex form)
[tex]f(x)-12=x^{2}-8x[/tex]
[tex]f(x)-12+16=x^{2}-8x+16[/tex]
[tex]f(x)+4=x^{2}-8x+16[/tex]
[tex]f(x)+4=(x-4)^{2}[/tex]
[tex]f(x)=(x-4)^{2}-4[/tex] ----> equation in vertex form
The vertex of the parabola is (4,-4)
so
The axis of symmetry is x=4
Part 2) The vertex of the equation above is also
we know that
The equation above is a vertical parabola open upward
therefore
The vertex is a minimum
Part 3) What is the vertex of the parabola described by the equation above
we know that
The equation of the parabola into vertex form is equal to
[tex]f(x)=(x-4)^{2}-4[/tex]
therefore
The vertex of the parabola is (4,-4)
Part 4) What are the x-intercepts of the parabola described by the equation above
we know that
The x-intercepts are the values of x when the value of y is equal to zero
so
[tex]f(x)+4=(x-4)^{2}[/tex]
f)x)=0
so
[tex]4=(x-4)^{2}[/tex]
take square root both sides
[tex](x-4)=(+/-)2[/tex]
[tex]x=4(+/-)2[/tex]
[tex]x=4(+)2=6[/tex]
[tex]x=4(-)2=2[/tex]
therefore
The x-intercepts are
(2,0) and (6,0)
