Find the vertex of the parabola f(x) = 2x squared minus 8x plus 1.

1. The vertex lies on the axis of symmetry, so its x-coordinate is negative b over 2a. 2. Here a is 2 and b is negative 8, so the x-coordinate is 8 divided by 4. 3. That gives an x-coordinate of 2. 4. Substitute 2 back into the function to get the matching output. 5. Two times 2 squared is 8, and negative 8 times 2 is negative 16. 6. Adding the constant gives 8 minus 16 plus 1, which is negative 7. 7. So the vertex sits at (2, -7). 8. The point (2, 7) drops a minus sign while adding the three pieces. 9. The point (4, -15) uses x equal to 4, which comes from forgetting the 2a denominator. _Source: OpenStax Intermediate Algebra (CC BY 4.0), section 9.6 Graph Quadratic Functions Using Properties_