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Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Solving Quadratic Equations: An Example Given the quadratic equation: \[ y = x^2 - 3x - 5 \] #### Solve to Find the Solutions: To solve the equation using the quadratic formula, we follow these steps: The quadratic formula is given by: \[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a} \] For the equation \( y = x^2 - 3x - 5 \), the coefficients are: - \( a = 1 \) - \( b = -3 \) - \( c = -5 \) Substitute these values into the quadratic formula: \[ x = \frac{{-(-3) \pm \sqrt{(-3)^2 - 4(1)(-5)}}}{2(1)} \] This simplifies to: \[ x = \frac{{3 \pm \sqrt{9 + 20}}}{2} \] \[ x = \frac{{3 \pm \sqrt{29}}}{2} \] #### Enter the number that belongs in the green box: \[ x = \frac{{3 \pm \sqrt{29}}}{2} \] From the choices provided: - A. 3 - B. 6 - C. -9 - D. 13 The number that belongs in the green box is **29**. Diagram Explanation: In the provided image, a quadratic equation is solved using the quadratic formula. Key steps involve substituting the coefficients \( a \), \( b \), and \( c \) into the quadratic formula, leading to a detailed step-by-step simplification. The green box marks the placeholder for the value computed under the square root, which in this case is \( 29 \). The multiple-choice options allow students to identify this value correctly. Note: The correct number that should be in the green box is the discriminant, \( \Delta = b^2 - 4ac = 29 \), used in solving the quadratic equation.
Transcribed Image Text:### Solving Quadratic Equations: An Example Given the quadratic equation: \[ y = x^2 - 3x - 5 \] #### Solve to Find the Solutions: To solve the equation using the quadratic formula, we follow these steps: The quadratic formula is given by: \[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a} \] For the equation \( y = x^2 - 3x - 5 \), the coefficients are: - \( a = 1 \) - \( b = -3 \) - \( c = -5 \) Substitute these values into the quadratic formula: \[ x = \frac{{-(-3) \pm \sqrt{(-3)^2 - 4(1)(-5)}}}{2(1)} \] This simplifies to: \[ x = \frac{{3 \pm \sqrt{9 + 20}}}{2} \] \[ x = \frac{{3 \pm \sqrt{29}}}{2} \] #### Enter the number that belongs in the green box: \[ x = \frac{{3 \pm \sqrt{29}}}{2} \] From the choices provided: - A. 3 - B. 6 - C. -9 - D. 13 The number that belongs in the green box is **29**. Diagram Explanation: In the provided image, a quadratic equation is solved using the quadratic formula. Key steps involve substituting the coefficients \( a \), \( b \), and \( c \) into the quadratic formula, leading to a detailed step-by-step simplification. The green box marks the placeholder for the value computed under the square root, which in this case is \( 29 \). The multiple-choice options allow students to identify this value correctly. Note: The correct number that should be in the green box is the discriminant, \( \Delta = b^2 - 4ac = 29 \), used in solving the quadratic equation.
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