Question 1209637
Here's how to find the vertex of the parabola:

1. **Simplify the function:**

Combine like terms in the given function:

f(x) = (2x² - 5x²) + (-13x + 19x) + (20 + 7)
f(x) = -3x² + 6x + 27

2. **Find the x-coordinate of the vertex:**

The x-coordinate of the vertex of a parabola in the form ax² + bx + c is given by:

x = -b / 2a

In our simplified equation, a = -3 and b = 6.  So:

x = -6 / (2 * -3)
x = -6 / -6
x = 1

3. **Find the y-coordinate of the vertex:**

Substitute the x-coordinate (x = 1) back into the simplified function to find the y-coordinate:

f(1) = -3(1)² + 6(1) + 27
f(1) = -3 + 6 + 27
f(1) = 30

4. **Vertex coordinates:**

The vertex of the parabola is (x, y) = (1, 30).

Therefore, the vertex of the parabola y = f(x) is $(1, 30)$.