Quadratic = 2nd Degree Polynomial.

$$y = x^2$$ $$y = ax^2 + bx + c$$ $$y = ax^2 + 2ax + a^2$$

To visualize:

• Solve for x to find the roots (where y = 0).
• The constant is the y-intercept.

Make the left-size into some expression squared, taking advantage of the fact that: $$(a+x)^2 = ax^2 + 2ax + a^2$$

Like this: \begin{align*} x^2 + 16x - 57 &= 0\\ x^2 + 16x + 64 &= 57+64\\ (x+8)^2 &= 121\\ \end{align*}

\begin{align*} ax^2 + bx + c &= 0\\ x &= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \end{align*}