What is the axis of symmetry for f(x) = -5x² - 20x - 10?

Solution:

Given, f(x) = -5x² - 20x - 10

We have to find the axis of symmetry for f(x).

Let y = -5x² - 20x - 10

Taking out common term,

y = -5(x² + 4x + 2)

y = -5(x² + 4x + 4 - 4 + 2)

y = -5[(x + 2)² - 2]

y = -5(x + 2)² + 10

y - 10 = -5(x + 2)²

(x + 2)² = -1/5(y - 10) --- (1)

The vertex form of equation of a parabola is given by

(x - h)² = 4a(y - k) --- (2)

Where, (h, k) is the vertex

Comparing (1) and (2),

h = -2

k = 10

The equation is a parabola having vertex at (h, k) = (-2, 10).

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

Therefore, the axis of symmetry is x = -2.

---

What is the axis of symmetry for f(x) = -5x² - 20x - 10?

Summary:

The axis of symmetry for f(x) = -5x² - 20x - 10 is x = -2.