Use a technique used to rewrite the quadratic function x2 + 6x + 8 from standard form to vertex form.
Quadratic equations are equations with a degree of two. They can be represented in the standard form ax2 + bx + c as well as in the vertex form a(x - h)2 + k = 0.
Answer: The equation x2 + 6x + 8 in vertex form is represented as [(x + 3)2 - 1].
Let's understand the solution. The technique used is completing the square method.
To convert the given standard equation to vertex form, we follow the below steps:
⇒ First, we identify the coefficient of x, that is, 6.
⇒ Now, we half and square the coefficient of x, that is, (6 / 2)2 = 9.
⇒ After this, we add and subtract the above result from the equation.
⇒ Now, we write the equation as (x2 + 6x + 9 - 9 + 8).
⇒ Now, using the identity of ( a + b)2 = a2 + 2ab + b2; we get (x2 + 6x + 9 - 9 + 8) = [(x + 3)2 - 1].
The above equation is the vertex form of the given equation. The vertex of the parabola representing the equation is the point (-3, -1).
Hence, The equation x2 + 6x + 8 in vertex form is represented as [(x + 3)2 - 1].