Objective
By the end of this lesson, you will be able to solve linear equations of up to 2 steps and quadratic equations of the form ax^2 + bx + c = 0.
Materials and Prep
- Pencil
- Eraser
- Blank paper
- Calculator (optional)
No prior knowledge is required for this lesson.
Activities
Warm-up: Solve simple linear equations with one step. For example, solve 2x + 3 = 9.
Practice solving linear equations with two steps. For example, solve 3x - 5 = 7.
Introduction to quadratic equations: Discuss the general form ax^2 + bx + c = 0 and its components.
Solve quadratic equations by factoring. Provide examples such as x^2 - 6x + 8 = 0.
Solve quadratic equations by using the quadratic formula. Demonstrate how to apply the formula to specific examples.
Challenge: Create your own quadratic equation and solve it using any method you prefer.
Talking Points
Linear equations involve unknowns (variables) and constants. We want to find the value of the variable that makes the equation true.
When solving linear equations, we perform operations to isolate the variable on one side of the equation.
Quadratic equations are equations of degree 2, meaning the highest power of the variable is 2.
Quadratic equations can have one, two, or no real solutions, depending on the discriminant (b^2 - 4ac).
We can solve quadratic equations by factoring, completing the square, or using the quadratic formula.
The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a). It gives us the solutions for any quadratic equation in the form ax^2 + bx + c = 0.
Remember to simplify your solutions and check your answers by substituting them back into the original equation.