Question

what is the axis of symmetry (aos) for (y = -x^2 + 6x + 2)?

• (x = 6)
• (x = 2)
• (x = 3)
• (x = -3)

Explanation:

🆕 New Concept Discovered: Axis of Symmetry of a Parabola
The vertical line that splits a parabola into two matching halves.

Step 1: Identify the coefficients

For a quadratic equation in standard form \( y = ax^2 + bx + c \), identify the values of \( a \) and \( b \):

$$ y = -1x^2 + 6x + 2 $$

$$ a = -1 $$

$$ b = 6 $$

Step 2: Apply the Axis of Symmetry formula

The formula to find the axis of symmetry (AOS) is:

$$ x = \frac{-b}{2a} $$

Substitute the values of \( a \) and \( b \) into the formula:

$$ x = \frac{-6}{2(-1)} $$

$$ x = \frac{-6}{-2} $$

$$ x = 3 $$

Answer:

\( x = 3 \)