Complete the square for the quadratic expression $2x^2 + 8x + 1$. Hence sketch the graph of the fu

Question

Complete the square for the quadratic expression $2x^2 + 8x + 1$.

Hence sketch the graph of the function
\[ f(x) = 2x^2 + 8x + 1, \]
where $x \in \mathbb{R}$.

Using the sketch, find the range of the function $f$.

Accepted Answer

$f(x)=2(x+2)^2-7;\quad R_f=[-7,\infty)$.

Graph of a quadratic function