Answer:
Part 1) "a" value is [tex]2[/tex]
Part 2) The vertex is the point [tex](1,8)[/tex]
Part 3) The equation of the axis of symmetry is [tex]x=1[/tex]
Part 4) The vertex is a minimum
Part 5) The quadratic equation in standard form is [tex]y=2x^{2}-4x+10[/tex]
Step-by-step explanation:
we know that
The equation of a vertical parabola into vertex form is equal to
[tex]y=a(x-h)^{2}+k[/tex]
where
(h,k) is the vertex of the parabola
if a > 0 then the parabola open upward (vertex is a minimum)
if a < 0 then the parabola open downward (vertex is a maximum)
The equation of the axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex
so
[tex]x=h[/tex]
In this problem we have
[tex]y=2(x-1)^{2}+8[/tex] -----> this is the equation in vertex form of a vertical parabola
The value of [tex]a=2[/tex]
so
a>0 then the parabola open upward (vertex is a minimum)
The vertex is the point [tex](1,8)[/tex]
so
[tex](h,k)=(1,8)[/tex]
The equation of the axis of symmetry is [tex]x=1[/tex]
The equation of a vertical parabola in standard form is equal to
[tex]y=ax^{2}+bx+c[/tex]
Convert vertex form in standard form
[tex]y=2(x-1)^{2}+8[/tex]
[tex]y=2(x^{2}-2x+1)+8[/tex]
[tex]y=2x^{2}-4x+2+8[/tex]
[tex]y=2x^{2}-4x+10[/tex]
see the attached figure to better understand the problem
