Question

Y=ˣ²-6x+8 on the uding the roots and the vertex

Answer 1

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).