Question

question
find the equation of the axis of symmetry of the following parabola algebraically.
$y = x^2 - 14x + 47$

Explanation:

Step1: Recall the formula for the axis of symmetry of a parabola in the form \(y = ax^2 + bx + c\). The formula is \(x = -\frac{b}{2a}\).

Here, the given equation is \(y = x^2 - 14x + 47\), so \(a = 1\) and \(b = -14\).

Step2: Substitute the values of \(a\) and \(b\) into the formula.

\(x = -\frac{-14}{2\times1}\)
Simplify the expression: \(x = \frac{14}{2} = 7\)

Answer:

The equation of the axis of symmetry is \(x = 7\)