What is the axis of symmetry for f(x) = -2x² + 20x - 42?

Solution:

Given, f(x) = -2x² + 20x - 42

Let y = -2x² + 20x - 42

y = -2(x² - 10x + 21)

y = -2(x² - 10x + 25 - 25 + 21)

y = -2[(x - 5)² - 4]

y = -2(x - 5)² + 8

(y - 8) = -2(x - 5)²

(x - 5)² = -1/2 (y - 8) ------(1)

This is of the form (x - h)² = 4a (y - k) ------(2)

∴ Comparing equations (1) and (2) the given equation is a parabola having vertex at (h, k) = (5, 8).

Axis is a line passing through a vertex perpendicular to x-axis that divides the parabola into two halves.

∴ Axis of symmetry is x = 5.

---

What is the axis of symmetry for f(x) = -2x² + 20x - 42?

Summary:

The axis of symmetry for f(x) = -2x² + 20x - 42 is x = 5.