Multiple Choice
Find the solution(s) using the quadratic formula.
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12. Quadratic Equations and Functions
The Quadratic Formula
Multiple Choice
Which would be the most appropriate method to solve the following equation?
A
Factoring
B
Square-Root Property
C
Quadratic Formula
D
Complete the Square
Verified step by step guidance1
Identify the quadratic equation you need to solve. A quadratic equation is generally in the form \(a x^{2} + b x + c = 0\), where \(a\), \(b\), and \(c\) are constants and \(a \neq 0\).
Examine the quadratic equation to decide which method to use for solving it. The common methods are factoring, completing the square, using the quadratic formula, or graphing.
If the quadratic can be factored easily (i.e., it factors into two binomials with integer coefficients), use factoring. Otherwise, consider completing the square or the quadratic formula.
Recall the quadratic formula: \(x = \frac{-b \pm \sqrt{b^{2} - 4 a c}}{2 a}\). This method works for all quadratic equations and is especially useful when factoring is difficult or impossible.
Once you choose the method, apply it step-by-step to find the values of \(x\) that satisfy the equation. Remember to check your solutions by substituting them back into the original equation.
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