Question

find the equation of the axis of symmetry of the following quadratic equation.
$f(x) = -\frac{14}{15}(x - 5)^2 - 2$

Explanation:

Step1: Recall vertex form of quadratic

The vertex form of a quadratic function is \( f(x) = a(x - h)^2 + k \), where \((h, k)\) is the vertex and the axis of symmetry is \( x = h \).

Step2: Identify \( h \) from given function

For the function \( f(x) = -\frac{14}{15}(x - 5)^2 - 2 \), comparing with \( a(x - h)^2 + k \), we see that \( h = 5 \).

Step3: Determine axis of symmetry

Using the formula for the axis of symmetry from the vertex form, since \( h = 5 \), the axis of symmetry is \( x = 5 \).

Answer:

\( x = 5 \)