Final answer:
The roots of the equation are x = 4 and x = 2. The vertex of the equation is (3, -1).
Step-by-step explanation:
This expression is a quadratic equation of the form ax²+bx+c = 0, where the constants are a = 1, b = -6, and c = 8. To find the roots, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
Plugging in the values, we get:
x = (-(-6) ± √((-6)² - 4(1)(8))) / (2(1))
x = (6 ± √(36 - 32)) / 2
x = (6 ± √4) / 2
x = (6 ± 2) / 2
x = (8 / 2) or (4 / 2)
x = 4 or 2
The roots of the equation are x = 4 and x = 2.
To find the vertex, we can use the formula x = -b / (2a). Plugging in the values, we get:
x = -(-6) / (2(1))
x = 6 / 2
x = 3
Substituting this value back into the original equation, we get:
y = (3)² - 6(3) + 8
y = 9 - 18 + 8
y = -1
The vertex of the equation is (3, -1).