Final answer:
To solve the quadratic equation (x + 2)² - 9 = 0, we use the quadratic formula to find the two possible values of x. The solutions are x = -2 + sqrt(36)/2 and x = -2 - sqrt(36)/2. The vertex of the equation is (-2, -9).
Step-by-step explanation:
To solve the quadratic equation (x + 2)² - 9 = 0, we first need to rewrite it in the form ax² + bx + c = 0. Expanding the equation, we get x² + 4x + 4 - 9 = 0. Simplifying further, we have x² + 4x - 5 = 0.
Next, we can find the roots of the quadratic equation by using the quadratic formula:
x = (-b ± sqrt(b² - 4ac)) / (2a)
Plugging in the values from our equation, we have:
x = (-4 ± sqrt(4² - 4(1)(-5))) / (2(1))
Simplifying further, we get x = (-4 ± sqrt(36)) / 2. Therefore, the two possible values for x are x = -2 + sqrt(36)/2 and x = -2 - sqrt(36)/2.
The vertex of a quadratic equation in the form y = a(x - h)² + k is given by the coordinates (h, k). In our equation, the vertex form is (x + 2)² - 9 = 0. Comparing this to the standard form, we can see that the vertex is at (-2, -9).