Question

Find the value of f(-6).yy = f(x)108642-10-8-6-422468.10-2-4-6-8

Answer 1

The given graph is a downward parabola.

The roots of the equation is -2 and -8, and the vertex is (-5,7).

The general root form of parabola will be,

a(x-(-2))(x-(-8))=a(x+2)(x+8).

The value of a can be determined from the coordinate of vertex,

$\begin{gathered} y=a(x+2)(x+8) \\ 7=a(-5+2)(-5+8) \\ 7=a\times(-3)(3) \\ a=\frac{-7}{9} \end{gathered}$

Thus, the required quadratic is,

$f(x)=\frac{-7}{9}(x+2)(x+8)$

The value of f(-6) can be determined as,

$\begin{gathered} f(-6)=\frac{-7}{9}(-6+2)(-6+8) \\ =6.22 \end{gathered}$

Thus, the requried value of f(-6) is 6.22.