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What are the points of intersection of the following parabolas y equals x2 -7x plus 8 and y equals -x2 plus 9x -6?
y = x2 - 7x + 8 y = -x2 + 9x - 6 subtract the 2nd from the 1st equation
0 = 2x2 - 16x + 14 simplify
0 = x2 - 8x + 7 factor it, since 7 = (-1)(-7) and -1 - 7 = -8
0 = (x - 1)(x - 7) let each factor equal to zero
x - 1 = 0 or x - 7 = 0 solve for x
thus, x = 1 and x = 7.
Chose one of the equation and substitute x with 1, and 7 to find the corresponding y-values.
y = x2 - 7x + 8
y = (1)2 - 7(1) + 8 = 1 - 7 + 8 = 2; (1, 2) intersection point
y = (7)2 - 7(7) + 8 = 49 - 49 + 8 = 8; (7, 8) intersection point
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What are the points of intersection of the parabolas of y equals 4x squared -12x -3 and y equals x squared plus 11x plus 5 on the Cartesian plane?
The points are (-1/3, 5/3) and (8, 3).Another Answer:-The x coordinates work out as -1/3 and 8Substituting the x values into the equations the points are at (-1/3, 13/9) and (8, 157)
What are the points of intersection of the parabolas y equals x squared -2x plus 4 and y equals 2x squared -4x plus 4?
If: y = x^2 -2x +4 and y = 2x^2 -4x +4 Then: 2x^2 -4x +4 = x^2 -2x +4 Transposing terms: x^2 -2x = 0 Factorizing: (x-2)(x+0) => x = 2 or x = 0 Therefore by substitution points of intersect are at: (2, 4) and (0, 4)
Which of the following points are on the line given by the equation y equals 2x?
(4,2), (2,1),(-2,-1)
Although locus of points can be used to define a straight line and circle more complex shapes such as parabolas must be defined a different way?
False
Why can three coplanar lines have zero one two or three points of intersection?
If all three lines are parallel, there are zero points of intersection. If all three lines go through a point, there is one point of intersection. If two lines are parallel and the third one crosses them, there are two. If the three lines make a triangle, there are three points.
What are the points of intersection of the parabolas of y equals 4x squared -12x -3 and y equals x squared plus 11x plus 5 on the Cartesian plane?
The points are (-1/3, 5/3) and (8, 3).Another Answer:-The x coordinates work out as -1/3 and 8Substituting the x values into the equations the points are at (-1/3, 13/9) and (8, 157)
What are the points of intersection of the line x -y equals 2 with x squared -4y squared equals 5?
The points of intersection are: (7/3, 1/3) and (3, 1)
What are the points of intersection of 3x -2y -1 equals 0 with 3x squared -2y squared equals -5 on the Cartesian plane?
Points of intersection work out as: (3, 4) and (-1, -2)
What are the points of intersection of the following parabolas y equals 4x squared -2x -1 and 2x squared equals 3x -y plus 5?
If: y = 4x^2 -2x -1 and 2x^2 = 3x -y +5 Then: 4x^2 -2x -1 = -2x^2 +3x +5 Transposing terms: 6x^2 -5x -6 = 0 Factorizing: (3x+2)(2x-3) = 0 => x = -2/3 or x = 3/2 By substitution points of intersection are at: (-2/3, 19/9) and (3/2, 5)
What is if any are the points of intersection of the parabolas y equals x2 -4x plus 8 and y equals 8x -x2 -14 showing work with explanations?
If: y = x2-4x+8 and y = 8x-x2-14 Then: x2-4x+8 = 8x-x2-14 So: 2x2-12x+22 = 0 Discriminant: 122-(4*2*22) = -32 Because the discriminant is less than 0 there is no actual contact between the given parabolas
Where are the points of intersection of the equations 4y squared -3x squared equals 1 and x -2y equals 1?
The points of intersection of the equations 4y^2 -3x^2 = 1 and x -2 = 1 are at (0, -1/2) and (-1, -1)
What are the points of intersection of the parabolas y equals 4x squared -2x -1 and y equals -2x squared plus 3x plus 5 showing work with answers?
If: y = 4x^2 -2x -1 and y = -2x^2 +3x +5 Then: 4x^2-2x-1 = -2x^2+3x+5 =>6x^2-5x-6 = 0 Solving the above quadratic equation: x = -2/3 or x = 3/2 Therefore by substitution the points of intersection are: (-2/3, 19/9) and (3/2, 5)
What are the points of intersection of the parabolas y equals 4x squared -2x -1 and y equals -2x squared plus 3x plus 5 showing work and answers?
If: y = 4x^2 -2x -1 and y = -2x^2+3x+5 Then: 4x^2 -2x -1 = -2x^2+3x+5 => 6x^2-5x-6 = 0 Solving the above quadratic equation: x = -2/3 or x = 3/2 Therefore the points of intersection by substitution are: (-2/3, 19/9) and (3/2, 5)
What are the points of intersection of the parabolas when y equals -2x squared plus 3x plus 5 and y equals 4x squared -2x -1 showing work?
If: y = -2x^2 +3x +5 and y = 4x^2 -2x -1 Then: 4x^2 -2x -1 = -2x^2 +3x +5 So it follows: 6x^2 -5x -6 = 0 Using the quadratic equation formula: x = -2/3 or x = 3/2 Therefore points of intersection by substitution are at: (-2/3, 19/9) and (3/2, 5)
What are the points of intersection of the parabolas y equals 4x squared -2x -1 and -2x squared plus 3x plus 5 showing key stages of work?
If: y = 4x2-2x-1 and y = -2x2+3x+5 Then: 4x2-2x-1 = -2x2+3x+5 So: 6x2-5x-6 = 0 Solving the quadratic equation: x = -2/3 or x = 3/2 Points of intersection by substitution: (-2/3, 19/9) and (3/2, 5)
What are the points of intersection between the equations of 3x -5y equals 16 and xy equals 7?
If 3x -5y = 16 and xy = 7 then by combining both equations into a single quadratic equation and solving it then the points of intersection are at (-5/3, -21/5) and (7, 1)
What points lies on the graph of the function y equals 4x?
Since there are no "following" points, none of them.
