Sketch the graph of the quadratic function $f(x) = 5 x^2 +3 x +1$ by hand.
Indicate on your sketch the coordinates of any turning points and of
any point where the graph crosses the $x$ or $y$ axis.
Your graph should look something like this.
There are no real roots
There is a minimum point at $x=-0.30$, $y=0.55$
The graph intercepts the $y$-axis at $y=1$