Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Connect with a community of experts ready to provide precise solutions to your questions quickly and accurately. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
To find the zeros of the quadratic equation [tex]\( y = x^2 + 4x - 9 \)[/tex] by completing the square, follow these steps:
1. Rewrite the equation:
[tex]\[ x^2 + 4x - 9 = 0 \][/tex]
Move the constant term to the other side of the equation:
[tex]\[ x^2 + 4x = 9 \][/tex]
2. Complete the square:
To complete the square, add and subtract the same value inside the equation. We take half of the coefficient of [tex]\( x \)[/tex], square it, and add it to both sides of the equation.
The coefficient of [tex]\( x \)[/tex] is 4. Half of 4 is 2, and [tex]\( 2^2 = 4 \)[/tex]. Thus, we add 4 to both sides:
[tex]\[ x^2 + 4x + 4 = 9 + 4 \][/tex]
[tex]\[ (x + 2)^2 = 13 \][/tex]
3. Solve for [tex]\( x \)[/tex] by taking the square root of both sides:
[tex]\[ x + 2 = \pm \sqrt{13} \][/tex]
[tex]\[ x = -2 \pm \sqrt{13} \][/tex]
So, the zeros of the equation [tex]\( y = x^2 + 4x - 9 \)[/tex] are:
[tex]\[ x = -2 + \sqrt{13} \quad \text{and} \quad x = -2 - \sqrt{13} \][/tex]
Therefore, the correct answer is:
[tex]\[ D. \, x = -2 \pm \sqrt{13} \][/tex]
1. Rewrite the equation:
[tex]\[ x^2 + 4x - 9 = 0 \][/tex]
Move the constant term to the other side of the equation:
[tex]\[ x^2 + 4x = 9 \][/tex]
2. Complete the square:
To complete the square, add and subtract the same value inside the equation. We take half of the coefficient of [tex]\( x \)[/tex], square it, and add it to both sides of the equation.
The coefficient of [tex]\( x \)[/tex] is 4. Half of 4 is 2, and [tex]\( 2^2 = 4 \)[/tex]. Thus, we add 4 to both sides:
[tex]\[ x^2 + 4x + 4 = 9 + 4 \][/tex]
[tex]\[ (x + 2)^2 = 13 \][/tex]
3. Solve for [tex]\( x \)[/tex] by taking the square root of both sides:
[tex]\[ x + 2 = \pm \sqrt{13} \][/tex]
[tex]\[ x = -2 \pm \sqrt{13} \][/tex]
So, the zeros of the equation [tex]\( y = x^2 + 4x - 9 \)[/tex] are:
[tex]\[ x = -2 + \sqrt{13} \quad \text{and} \quad x = -2 - \sqrt{13} \][/tex]
Therefore, the correct answer is:
[tex]\[ D. \, x = -2 \pm \sqrt{13} \][/tex]
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.