use completing the square to describe the graph of each function.
How do you complete the square with this equations. please show me step by step so that I can understand it.
x^2-4x+6
x^2 - 4x + 6
first, yo only focus on the first two terms: x^2 and -4x. let's put a parenthesis to enclose them:
(x^2 - 4x) + 6
now, to complete the square, what we do is get the half of b (b is the numerical coefficient of x, and in this case, is -4) and we square it: (-4/2)^2 = 4. Then we add a term +4 inside the parenthesis, but to remain the value of the whole expression constant, we also put a -4 but outside the parenthesis:
(x^2 - 4x + 4) + 6 - 4
the term inside the parenthesis is a perfect square, and we can further simplify this into:
(x-2)^2 + 2
hope this helps~ :)
To complete the square for the equation x^2 - 4x + 6, follow these steps:
Step 1: Identify the coefficient of x^2. In this case, it is 1.
Step 2: Divide the coefficient of x by 2, square the result, and add it to both sides of the equation:
x^2 - 4x + 6 + (4/2)^2 = (4/2)^2
Simplifying further, we have:
x^2 - 4x + 4 + 6 = 4
Step 3: Rewrite the equation as a perfect square trinomial:
(x^2 - 4x + 4) + 6 = 4
(x - 2)^2 + 6 = 4
Step 4: Move the constant term to the other side of the equation:
(x - 2)^2 = 4 - 6
(x - 2)^2 = -2
Step 5: Take the square root of both sides:
√[(x - 2)^2] = ±√(-2)
x - 2 = ±√(-2)
Step 6: Simplify the square root of -2:
√(-2) = ±√2i
Step 7: Solve for x:
x - 2 = ±√2i
Adding 2 to both sides:
x = 2 ± √2i
The graph of the function y = x^2 - 4x + 6 is a parabola that opens upwards. The vertex of the parabola is at the point (2, 6).