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3 years ago

6

What patterns can you find between the coordinates of any point located in Quadrant one and coordinates of any Point located in

quadrant three

1 answer:

Dafna1 [17]3 years ago

5 0

Points on quadrant 1 always have positive coordinates while those in quadrant 3 always have negative coordinates

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3 years ago

Determine the next step for solving the quadratic equation by completing the square

GaryK [48]

Answer:

The two solutions are: $x=\frac{1}{2}+/-\frac{\sqrt{7} }{2}$

The next and every step are below.

Explanation:

1. $-3=-2x^2+2x$ : Given (addition property / add - 3 to both sides)

2. $-3 = - 2(x^2-x)$ : Given (commom factor - 2)

3. $-3-1/2=-2(x^2-x+1/4)$

To obtain the perfect square it was added the square of half of the coefficient of x: (1/2)² = 1/4, inside the parenthesis.

Since, the terms inside the parentthesis are multiplied by - 2, you have to add - 2 (1/4) = - 1/2 to the left side of the equation.

4. Now, you have that the trinomial x² - x + 1/4 is a square perfect trinomial which is factored as (x - 1/2)² and get the expression:

$-7/2=-2(x-1/2)^2$

5. Divide both sides by - 2 to get the next expression:

$-7/4=(x-1/2)^2$

6. The last step is to extract squere root from both sides of the equality:

$(x-1/2)=+/-\sqrt{\frac{7}{4}}\\ \\ x-1/2=+/-\frac{\sqrt{7} }{2}\\ \\ x=\frac{1}{2}+/-\frac{\sqrt{7} }{2}$

8 0

2 years ago