Q.Find the domain and range of the function $f(x)=7x^2+4x-1$.

$f(x)=7x^2+4x-1$ is a polynomial, so its domain is all of $R$.

Since $a=7>0$, the parabola opens upward, so its range is $[k,\infty)$ where $k$ is the minimum value, occurring at the vertex $x=-\dfrac{b}{2a}=-\dfrac{4}{14}=-\dfrac27$. …

Domain of any polynomial is always $R$; for the range, locate the vertex at $x=-b/2a$ and evaluate …

Using the vertex formula $\left(\dfrac{4ac-b^2}{4a},\infty\right)$ from the summary table but slipping on the arithmetic of $4ac-b^2$ — it is of …