We first identify that `a = 2`, `b = -8` and `c = 6`.

Step (a)

Since `a = 2`, `a > 0` hence the function is a parabola with a minimum point and it opens upwards (U-shaped)

Step (b)

The x co-ordinate of the minimum point is:

`x=b/(2a)=(-(-8))/(2(2))=8/4=2`

The y value of the minimum point is

`y = 2(2)^2 - 8(2) + 6 = -2`

So the minimum point is `(2, -2)`

Step (c)

The y-intercept is found by substituting `x = 0` into the y expression.

`y = 2(0)^2 - 8(0) + 6 = 6`

So `(0, 6)` is the y-intercept.

Step (d)

The x-intercepts are found by setting `y = 0` and solving:

`2x^2 - 8x + 6 = 0`

`2(x^2 - 4x + 3) = 0`

`2(x - 1)(x - 3) = 0`

So `x = 1`, or `x = 3`.

Using the above information, the sketch of the curve will be :

123456-1-25101520-5xy(0,6)(1,0)(3,0)Open image in a new page

`y = 2x^2 -8x + 6`, a U-shaped parabola, showing intersections with axes