Question

Given the quadratic equation
`y = 2(x -1)^(2) + 8`

Answer the following questions

"a" value =
Vertex =
Axis of Symmetry: x =
minimum or maximum (spelling counts):
Standard form = ___ x^2 - ___ x + ___

Image attached to better understand answering.

Answer 1

Part 1) "a" value is
`2`

Part 2) The vertex is the point
`(1,8)`

Part 3) The equation of the axis of symmetry is
`x=1`

Part 4) The vertex is a minimum

Part 5) The quadratic equation in standard form is
`y=2x^(2)-4x+10`

Explanation:

we know that

The equation of a vertical parabola into vertex form is equal to

`y=a(x-h)^(2)+k`

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

`x=h`

In this problem we have

`y=2(x-1)^(2)+8` -----> this is the equation in vertex form of a vertical parabola

The value of
`a=2`

so

a>0 then the parabola open upward (vertex is a minimum)

The vertex is the point
`(1,8)`

so

`(h,k)=(1,8)`

The equation of the axis of symmetry is
`x=1`

The equation of a vertical parabola in standard form is equal to

`y=ax^(2)+bx+c`

Convert vertex form in standard form

`y=2(x-1)^(2)+8`

`y=2(x^(2)-2x+1)+8`

`y=2x^(2)-4x+2+8`

`y=2x^(2)-4x+10`

see the attached figure to better understand the problem