All Things Being Equal

Learning Focus

Solve quadratic equations by graphing connections, factoring, square roots, and completing the square.

Big idea

$x$-intercepts of $f(x)$ are solutions of $f(x)=0$.

Useful tools:

• factor + zero product property
• rewrite as $(x-h)^2=k$ and take square roots
• complete the square, then use inverse operations

Worked example

$x^2-9x+20=0=(x-4)(x-5)$ so $x=4$ or $x=5$.

Takeaways

• Factored form makes intercepts obvious.
• Vertex form makes square-root solving natural.