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]
