It works out exactly as: 7 times the square root of 26
it will form a parabola on the graph with the vertex at point (0,0) and points at (1,1), (-1,1), (2,4), (-2,4)......
(6, 40) and (-1, 5)
Straight line: 3x-y = 5 Curved parabola: 2x^2 +y^2 = 129 Points of intersection works out as: (52/11, 101/11) and (-2, -11)
Equations: x2+2x-7 = 17-3x Quadratic equation: x2+5x-24 = 0 Points of intersection: (-8, 41) and (3, 8) Length of line: (-8-3)2+(41-8)2 = 1210 and the square root of this is the length of the line which is about 34.78505426 or to be exact it is 11 times the square root of 10.
The points of intersection are: (7/3, 1/3) and (3, 1)
Points of intersection work out as: (3, 4) and (-1, -2)
Coordinates: (-1, 5) and (6, 40) Length of line: 7 times the square root of 26 which is 35.693 to 3 d.p.
If: y = 17-3x and y = x^2+2x-7 Then: x^2+2x-7 = 17-3x => x^2+5x-24 = 0 Solving the quadratic equation: x = -8 and x = 3 Points of intersection with the parabola: (-8, 41) and (3, 8) Length of line: square root of [(-8-3)^2+(41-8)^2] = 34.785 to 3 d.p.
y = 5x +10 y = x2+4 Merge the two equations together to form a quadratic equatioin in terms of x. Solving the quadratic equation gives x = -1 or x = 6 So by substituting: when x = -1 then y = 5 and when x = 6 then y = 40 Therefore the line meets the parabola at points (-1, 5) and (6, 40) Length of line is the square root of the sum of (6 - -1)2+(40 -5)2 Length of line = 7 times the square root of 26 which is about 35.693 to 3 d.p.
7*sqrt(2) = 9.899 to 3 dp
They are the x-values (if any) of the points at which the y-value of the equation representing a parabola is 0. These are the points at which the parabola crosses the x-axis.
If: y = x^2 +2x -7 and y = 17 -3x Then: x^2 +2x -7 = 17 -3x => x^2 +5x -24 = 0 Solving the equation: x = 3 or x = 8 Points of intersection: (3, 8) and ( -8, 41) Length of line: square root of 1210 which is about 34.785 to three decimal places