Multiple Choice
Determine the number and type of solutions of the given quadratic equation. Do not solve.
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12. Quadratic Equations and Functions
The Quadratic Formula
Multiple Choice
Determine the most appropriate method and solve the following equation.
A
Factoring;
B
Square-Root Property;
C
Quadratic Formula;
D
Quadratic Formula;
Verified step by step guidance1
Identify the quadratic equation you need to solve. A quadratic equation is generally in the form \(ax^2 + bx + c = 0\), where \(a\), \(b\), and \(c\) are constants and \(a \neq 0\).
Examine the quadratic equation to decide which method to use: factoring, completing the square, or the quadratic formula. For example, if the equation factors easily, factoring is often quickest.
If factoring is not straightforward, check if completing the square is convenient by isolating the \(x^2\) and \(x\) terms and preparing to add a constant to both sides to form a perfect square trinomial.
If neither factoring nor completing the square seems simple, use the quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\). This method works for all quadratic equations.
After choosing the method, apply it step-by-step to find the values of \(x\) that satisfy the equation, remembering to simplify your answers as much as possible.
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