Final answer:
a. The vertex of the quadratic equation x² + 18x + 8 = 0 is at (-9, -73).
b. The equation in vertex form is y = (x + 9)² - 73.
Step-by-step explanation:
To find the vertex of the quadratic equation x² + 18x + 8 = 0, we use the formula x = -b/(2a) for the x-coordinate of the vertex, where a is the coefficient of x² and b is the coefficient of x.
In this case, a = 1 and b = 18, so the x-coordinate of the vertex is x = -18/(2×1) = -9.
To find the y-coordinate, we substitute x = -9 back into the original equation, yielding the y-coordinate as y = (-9)² + 18(-9) + 8 = 81 - 162 + 8 = -73.
Therefore, the vertex is at (-9, -73).
To write the quadratic in vertex form, we complete the square for the quadratic equation.
Vertex form is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.
Starting with the original equation x² + 18x + 8 = 0, we can rearrange and complete the square to get (x + 9)² - 73 = 0 or y = (x + 9)² - 73, which is now in vertex form.
Therefore, the equation in vertex form is y = (x + 9)² - 73.