Question

Find the equation of the quadratic function g whose graph is shown below.

Answer 1

`$f(x)=-3(x-5)^2+6$`

Explanation:

`$$Consider the formula for the vertex form of a parabola: \begin{center}$f(x)=a(x-h)^2+k$\end{center} Here, h is the x-coordinate of the vertex, and k is the y-coordinate of the vertex. \\\\\textbf{Step 1.} Substitute the points of the vertex into the above formula. \begin{center} $f(x)=a(x-5)^2+6$\end{center}\\`

`$$\textbf{Step 2.} Find the value of $a$ using the second point on the graph. We can do this by substituting 3 for $f(x)$ and 6 for $x$ in the above equation:\begin{center}$3=a(6-5)^2+6\\\Rightarrow3=a(1)^2+6\\\Rightarrow3=a+6\\\Rightarrow a=-3$\end{center}\\Now, substituting $a=-3$ into the original equation:\begin{center}\\\fbox{$f(x)=-3(x-5)^2+6$}\end{center}\\This is the final solution.`