Write the equation (x-1)2 = 2x in standard form and write the values of a, b and c.
Answers
Answer:
What is the linear standard form?
This is the standard form of linear equations in two variables:
\blueD ax+\greenD by=\goldD cax+by=cstart color #11accd, a, end color #11accd, x, plus, start color #1fab54, b, end color #1fab54, y, equals, start color #e07d10, c, end color #e07d10
Usually in this form, \blueD aastart color #11accd, a, end color #11accd, \greenD bbstart color #1fab54, b, end color #1fab54, and \goldD ccstart color #e07d10, c, end color #e07d10 are all integers.
Want to learn more about standard form? Check out this video.
Finding features and graph from standard equation
When we have a linear equation in standard form, we can find the xxx- and yyy-intercepts of the corresponding line. This also allows us to graph it.
Consider, for example, the equation \blueD2x+\greenD3y=\goldD{12}2x+3y=12start color #11accd, 2, end color #11accd, x, plus, start color #1fab54, 3, end color #1fab54, y, equals, start color #e07d10, 12, end color #e07d10. If we set x=0x=0x, equals, 0, we get the equation \greenD3y=\goldD{12}3y=12start color #1fab54, 3, end color #1fab54, y, equals, start color #e07d10, 12, end color #e07d10, and we can quickly tell that y=4y=4y, equals, 4, which means the yyy-intercept is (0,4)(0,4)left parenthesis, 0, comma, 4, right parenthesis.
In a similar way, we can set y=0y=0y, equals, 0 to get \blueD2x=\goldD{12}2x=12start color #11accd, 2, end color #11accd, x, equals, start color #e07d10, 12, end color #e07d10 and find that the xxx-intercept is (6,0)(6,0)left parenthesis, 6, comma, 0, right parenthesis. Now we can graph the line: