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Solving Quadratic Equations \( \begin{array}{l}\text { Which of the following statements are true when Solving Quadratic Equations? Check all } \\ \text { that apply. } \\ \text { To use the Quadratic Formula, you need to plug the values of } a \text {, } b \text {, and } c \text { into a } \\ \text { formula } \\ \text { To use the Quadratic Formula, you need to find the values of } a, b \text {, and } c \\ \text { One method of solving a quadratic equation is by Factoring } \\ \text { One method of solving a quadratic equation is by using the Quadratic Formula } \\ \text { To use the Quadratic Formula, you need to have the equation in standard form } \\ \text { Question Help: D Post to forum } \\ \text { Submit Question }\end{array} \)

Ask by Ward Haynes. in the United States
Mar 09,2025

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Answer

All the statements about solving quadratic equations are true.

Solution

1. The statement "To use the Quadratic Formula, you need to plug the values of \(a\), \(b\), and \(c\) into a formula" is true because the quadratic formula \[ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \] requires these values. 2. The statement "To use the Quadratic Formula, you need to find the values of \(a\), \(b\), and \(c\)" is true. In order to correctly identify the coefficients from an equation (typically written in standard form \( ax^2+bx+c=0 \)), you must determine \(a\), \(b\), and \(c\). 3. The statement "One method of solving a quadratic equation is by Factoring" is true because factoring is a common method used to solve quadratics when the expression can be written as a product of two binomials. 4. The statement "One method of solving a quadratic equation is by using the Quadratic Formula" is true as well. When factoring is not straightforward, the quadratic formula provides a reliable alternative. 5. The statement "To use the Quadratic Formula, you need to have the equation in standard form" is also true since the formula assumes the equation is of the standard form \( ax^2+bx+c=0 \). Thus, all of the statements are true.

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Mind Expander

Did you know that the Quadratic Formula, \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), derives from completing the square on the general form of a quadratic equation? This formula is like a magic wand for finding the roots of any quadratic equation, as long as you can identify the coefficients \( a \), \( b \), and \( c \)! In the real world, quadratic equations pop up in many exciting situations! From calculating the trajectory of a basketball shot to optimizing areas in business problems, understanding how to solve these equations can unlock valuable insights. You never know when you might need to find the maximum height of a rocket or the best design for a garden!

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