Formula for Success

Learning Focus

Understand and use the quadratic formula for $ax^2+bx+c=0$:

$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

Big idea

Completing the square on the general equation produces one formula that works for every quadratic.

The discriminant $D=b^2-4ac$ predicts the number/type of real solutions.

Takeaways

• Identify $a$, $b$, $c$ carefully (include signs).
• Simplify radicals when possible.
• Connect solutions back to $x$-intercepts on the graph.