Given the quadratic equation $3x^2-7x+2=0$, what are the values of $a$, $b$, and $c$, given $a{x}^2+bx+c=0$?

Use the quadratic formula to solve $x^2-4x+3=0$.

Solve $\frac{1}{2}{x}^2+2x-3=0$ using the quadratic formula and simplify your answers.

Find the complex roots of $x^2+4x+13=0$ and express them in the simplest $a+bi$ form.

A projectile's height (in meters) after $t$ seconds is modeled by $h\left(t\right)=-5t^2+20t+15$. Use the quadratic formula to find when $h\left(t\right)=0$. Identify which (if any) is physically meaningful.