Question

question
find the equation of the axis of symmetry of the following parabola algebraically.
$y = -x^2 + 8x$

Explanation:

Step1: Recall the formula for axis of symmetry

For a quadratic function in the form \( y = ax^2 + bx + c \), the equation of the axis of symmetry is \( x = -\frac{b}{2a} \).

Step2: Identify a and b from the given equation

In the equation \( y = -x^2 + 8x \), we have \( a = -1 \) and \( b = 8 \).

Step3: Substitute a and b into the formula

Substitute \( a = -1 \) and \( b = 8 \) into \( x = -\frac{b}{2a} \):

$$ x = -\frac{8}{2\times(-1)} = -\frac{8}{-2} = 4 $$

Answer:

The equation of the axis of symmetry is \( x = 4 \)