Question

If f(x) = (x + 2)² - 8(x + 2) + 7 in an orthonormal system, and the equation of the line is x = a, what is the value of a if it represents an axis of symmetry of the curve (C)?

A) 2
B) -2
C) 8
D) -8

Answer 1

To find the axis of symmetry for the curve given by the function f(x) = (x + 2)² - 8(x + 2) + 7, you complete the square to get the vertex form and determine that the axis of symmetry is x = 2.

Step-by-step explanation:

The function given is f(x) = (x + 2)² - 8(x + 2) + 7. To find the axis of symmetry of the curve (C), we need to complete the square to rewrite the equation in vertex form, which is y = a(x - h)² + k, where (h, k) is the vertex of the parabola, and the line x = h is the axis of symmetry.

Let's complete the square for the given function:

1. Rewrite the function in the form of a square and a constant: f(x) = [(x + 2) - 4]² - 16 + 7
2. Simplify the function: f(x) = (x - 2)² - 9
3. Therefore, the vertex form is f(x) = (x - 2)² - 9, and the vertex is at (2, -9)
4. The axis of symmetry is therefore x = 2

So the value of a representing the axis of symmetry of the curve is 2.