Question

What is the equation for the axis of symmetry for the function f(x)=5(x-35)(x+27)?

Answer 1

start by writing the function in standard form

`\begin{gathered} f(x)=5(x-35)(x+27) \\ f(x)=(5x-175)(x+27) \\ f(x)=5x^2+135x-175x-4725 \\ f(x)=5x^2-40x-4725 \end{gathered}`

The axis of symmetry for a quadratic equation is found in the h of the vertex (h,k)

according to this the vertex can be found by:

`\begin{gathered} (h,k)=(-(b)/(2a)\text{.f}(-(b)/(2a))) \\ h=-((-40))/(2\cdot5) \\ h=(40)/(10) \\ h=4 \end{gathered}`

The axis of symmetry can be found at x=4