1. Write a quadratic equation that can be solved by factoring. Solve your equation and show and explain all your work.
2. In this unit you have learned about several different ways to solve quadratic equations. How do you determine which method to use when you’re trying to solve a quadratic equation?
1. The quadratic equation that can be solved by factoring is:
x^2 + 6x + 8 = 0
To solve this equation by factoring, we need to find two numbers that multiply to give 8 and add up to 6. These numbers are 2 and 4. Therefore, we can rewrite the equation as:
(x + 2)(x + 4) = 0
Now we can use the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero and solve for x:
x + 2 = 0 or x + 4 = 0
x = -2 or x = -4
Thus, the solutions to the quadratic equation x^2 + 6x + 8 = 0 are x = -2 and x = -4.
2. The method we choose to solve a quadratic equation can depend on several factors, such as the form of the equation and the available tools or resources. For example, if the quadratic equation is already in standard form (ax^2 + bx + c = 0), we might choose to use the quadratic formula because it can be applied directly without any further manipulation. On the other hand, if the quadratic equation can be easily factored, we might choose to use factoring because it can be a quicker and more efficient method. Additionally, if we are given a graph or table of values, we might choose to use graphical methods such as finding intercepts or using the graph to estimate solutions. Ultimately, the method we choose should be based on the specific problem and our own strengths and preferences.