What's 3(x-2) (x-2)=0 can someone show me how to do this
2 answers:
Answer:
Step-by-step explanation:
The three does nothing. When the equation is y = 3(x - 2)(x - 2) then the graph is stretched. See below for the imported graph.
To make this graph = 0 you make (x - 2) = 0
x - 2 = 0 Add 2 to both sides
x - 2 + 2 = 0 + 2 Simplify
x = 2
As you can see from the graph, the lowest point is 2,0. It just touches the x axis. That happens because there are 2 roots, both the same.
Graph
Red: (x - 2)(x - 2)
Blue:3(x - 2)(x- 2)
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<h3>Answer:</h3>
y = 8x² -4x +4
<h3>Explanation:</h3>I find it quick and easy to let a graphing calculator do quadratic regression on the given points. It gives the coefficients of the equation directly. (See attached.)
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If you want to do this "by hand," you can substitute each of the x and y value pairs into the equation to get three linear equations in a, b, and c. These are generally easy to solve, as the "c" variable can be eliminated right away.
<em>For x = 2</em>
... 28 = a·2² +b·2 +c = 4a +2b +c
<em>For x = 4</em>
... 116 = a·4² +4b +c = 16a +4b +c
<em>For x = -3</em>
... 88 = a·(-3)² +b·(-3) +c = 9a -3b +c
Subtracting the first and third equations from the second, we have ...
... (16a +4b +c) -(4a +2b +c) = (116) -(28) ⇒ 12a +2b = 88
... (16a +4b +c) -(9a -3b +c) = (116) -(88) ⇒ 7a +7b = 28
Dividing the first of these reduced equations by 2, and the second by 7, we have ...
- 6a +b = 44
- a +b = 4
Subtracting the second of these from the first gives ...
... (6a +b) -(a +b) = (44) -(4) ⇒ 5a = 40
From which we find
... a = 8
... b = 4 -a = 4 -8 = -4
We choose the first of the original equations to find c:
... c = 28 -4a -2b = 28 -4·8 -2(-4)
... = 28 -32 +8 = 4
With (a, b, c) = (8, -4, 4), the equation of the parabola is ...
... y = 8x² -4x +4
<h2>Answers / Step-by-step explanation:</h2><h3>a. What is the length of one side of the square.</h3>
<em>Looking at the image, the radius (r) of the circle appears to cover half of the length of a side of the square. Hence, the side of the square has a length of </em><em>2r</em><em>.</em>
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<h3>b. The formula A= πr² is used to find the area of a circle. The formula A=4r² can be used to find the area of the square. Write the ratio of the area of the circle to the area of the square in the simplest form.</h3><em />.
<em>Notice that the value "r²" disappears from the expression because is being multiplied and divided by it at the same time.</em>
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c. Complete the table.
<em>To complete each cell of the table, simply take the equation of the asked parameter and substitute the value of r by the number indicated in the title of the column. For example, column 3 should be filled out like this:</em>
Area of Circle (units²): π(3)²or 9π.
Length of 1 Side of the Square: 2r= 2(3)= 6.
Area of Square (units²)= 4r²= 4(3)²= 36.
Ratio: .
<em>Do the same for all the other columns. </em>
<em>The answers to the table are presented on the attached image</em><em>.</em>
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d. What can you conclude about the relationship between the area of the circle and the square?
<em>They will always have the same value, π/4, regardless of the size of the square and circle. As long as the circle borders meet the square's at the middle of each side of the square, the relationship will be the same</em><em>.</em>