Lesson 18
Solving Quadratics
- Let’s work to solve quadratic equations.
18.1: Math Talk: Operations with Roots
Evaluate mentally:
\sqrt{100}-15
\sqrt{125-10^2}
20-2\sqrt{49}
\sqrt{4^2+3^2}
18.2: Checking Brother’s Work
Priya's older brother is working on some higher-level math work and claims that x = 3 is a solution to the equation x^3 - 5x^2 -2x = \text{-}24.
- Explain how she could check that his solution is correct using each of these tools.
- A basic calculator
- A graphing tool
- When looking at his work, Priya sees that he has the equation (x-3)(x^2 -2x - 8) = 0. Knowing the zero product property holds, Priya recognizes that this equation means x-3 = 0 or x^2 -2x - 8 = 0 for this question. Find 2 other solutions to the original equation. Explain or show your reasoning.
18.3: Steps to Using the Quadratic Formula
The quadratic formula solves equations of the form ax^2 + bx + c = 0 using the equation x=\frac{\text{-}b \pm \sqrt{b^2 - 4ac}}{2a}.
Andre wants to use the quadratic formula to solve x^2 - 7x = \text{-}12.
- What should Andre do first?
- What values of a, b, and c should he use?
- After substituting the values into the quadratic formula, what is the order he should use to calculate the solutions?
- Use the quadratic formula to solve the equation.
- Check your solutions.