Notes
No matter, one formula can solve ANY quadratic equation of the form
𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0
where a, b, and c are integers. However, it’s a little complicated looking…
For any quadratic of the form 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0, the quadratic formula is…
Let’s start out with the basics. Identify the a, b, and c for the following quadratics.
1) 5𝑥 2 + 7𝑥 + 1 = 0
2) 2𝑥 2 − 6𝑥 + 11 = 0
3) −𝑥 2 + 𝑥 − 2 = 0
4) −3𝑥 2 − 𝑥 + 5 = 0
5) 10 − 6𝑥 + 𝑥 2 = 0
6) 8𝑥 2 − 5 = 6𝑥
Once we’re able to label our a, b, and c, we can plug in these values to the quadratic
formula. Let’s try it!
Example 1: Solve 2𝑥 2 + 𝑥 − 4 = 0. Round to the nearest hundredth, if necessary.
Step 1: Label your a, b, and c.
Step 2: Plug in your values into the quadratic formula. Leave yourself plenty of room!
Step 3: Simplify and put into { }.
You try! Solve 5𝑥 2 + 2𝑥 − 3 = 0. Round to the nearest hundredth, if necessary.
Step 1:
Step 2:
Step 3: