Determine the x-intercepts of the following equation.left bracket, x, minus, 4, right bracket, left bracket, x, minus, 3, right bracket, equals, y(x−4)(x−3)=yAnswerMultiple Choice Answersleft bracket, 12, comma, 0, right bracket(12,0)left bracket, 0, comma, 12, right bracket(0,12)left bracket, 4, comma, 0, right bracket, and , left bracket, minus, 3, comma, 0, right bracket(4,0) and (−3,0)left bracket, 0, comma, 4, right bracket, and , left bracket, 0, comma, 3, right bracket(0,4) and (0,3)left bracket, 4, comma, 0, right bracket, and , left bracket, 3, comma, 0, right bracket(4,0) and (3,0)left bracket, 0, comma, minus, 12, right bracket(0,−12)
Question
Determine the x-intercepts of the following equation.left bracket, x, minus, 4, right bracket, left bracket, x, minus, 3, right bracket, equals, y(x−4)(x−3)=yAnswerMultiple Choice Answersleft bracket, 12, comma, 0, right bracket(12,0)left bracket, 0, comma, 12, right bracket(0,12)left bracket, 4, comma, 0, right bracket, and , left bracket, minus, 3, comma, 0, right bracket(4,0) and (−3,0)left bracket, 0, comma, 4, right bracket, and , left bracket, 0, comma, 3, right bracket(0,4) and (0,3)left bracket, 4, comma, 0, right bracket, and , left bracket, 3, comma, 0, right bracket(4,0) and (3,0)left bracket, 0, comma, minus, 12, right bracket(0,−12)
Solution
The x-intercepts of an equation are the points where the graph of the equation crosses the x-axis. This happens when y = 0.
Given the equation (x−4)(x−3)=y, we set y = 0 and solve for x:
0 = (x−4)(x−3)
This equation is satisfied when x - 4 = 0 or x - 3 = 0.
Solving these equations gives x = 4 and x = 3.
Therefore, the x-intercepts of the equation are (4,0) and (3,0).
So, the correct answer is "left bracket, 4, comma, 0, right bracket, and , left bracket, 3, comma, 0, right bracket(4,0) and (3,0)".
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