Follow these steps to draw a parabola with the given equation: *y = 2*^{2 }*− 4x + 1*

###### 1. Identify the Coefficients

In this case, *a* is 2, *b* is -4 and *c* is 1.

*a* determines if the parabola opens up or down. In this case, it opens up since it's a positive number.*b* determines the tilt or slant of the parabola.*c* is a constant term that shifts the parabola up or down.

###### 2. Find the Vertex

The parabola's vertex is (*h*,*k*). This is about to get really confusing, so hang in there with us: *h* is the x-coordinate of the vertex, and *k* is the vertex's y-coordinate. Keep that in mind for the rest of this step.

Now, *h = -b/2a*. Plug in the values into the formula, and you get:

This means the x-coordinate of the vertex is 1. Now, find *k*, the y-coordinate of the vertex, by substituting *h* back into the original expression (*ax*^{2}* + bx + c*):

This makes the vertex (1, -1).

###### 3. Determine the Axis of Symmetry

The parabola's axis of symmetry (*x = h*) is a vertical line passing through the vertex, so as demonstrated above, this is *x = 1*.

###### 4. Calculate the X-intercepts

You can solve it using the quadratic formula: *x = -b ± √(b² – 4ac) / (2a)*. Substitute the values of *a*, *b* and *c* into the formula.

*x = -(-4) ± √((-4)² – 4(2)(1)) / 2(2)*

Then you calculate the two x-intercepts: one for *a* + and one for *a* –.

*x = 4 + (2√2) / 4 = 4 + (√2)/2*

*x = 4 – (2√2) / 4 = 4 + (√2)/2*

So the x-intercepts are: *2 + (√2)/2* and *2 – (√2)/2*.

###### 5. Calculate the Y-intercept

To find the y-intercept, set *x* to 0 and solve for *y*.

This makes the y-intercept point is (0,1).