Question 1209638: What is the equation of the line of symmetry of the parabola $y = f(x)$.
f(x) = 2x^2 - 13x + 20 - 5x^2 + 19x + 7. Answer by CPhill(1959) (Show Source):
You can put this solution on YOUR website! Here's how to find the equation of the line of symmetry:
1. **Simplify the quadratic 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 line of symmetry for a parabola is a vertical line that passes through 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. **Equation of the line of symmetry:**
The line of symmetry is a vertical line with the equation x = (x-coordinate of the vertex). Therefore, the equation of the line of symmetry is:
x = 1
