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)......
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)
Coordinates: (-1, 5) and (6, 40) Length of line: 7 times the square root of 26 which is 35.693 to 3 d.p.
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.
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.
Points of intersection work out as: (3, 4) and (-1, -2)
A parabola has one vertex (but not in the sense of an angle), infinitely many points and no edges.
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.
First find the points of intersection of the two equations: 17 - 3x = x2 + 2x - 7 or x2 + 5x - 24 = 0 This has the solutions x = 3 and x = -8 So the coordinates of the two points of intersection are (3,8) and (-8,41). Then, by Pythagoras, the length is sqrt[(3+8)2 + (8-41)2] = sqrt(121 + 1089) = sqrt(1210) = 11 sqrt(10) or 34.785 units (approx).
If: y = x^2+4 and y = 5x+10 Then: x^2+4 = 5x+10 So: x^2-5x-6 = 0 => x = -1 or x = 6 Points of intertsection by substitution: (6, 40 and (-1, 5) Length of line: sq rt of (6--1)^2+(40-5)^2 = 7 times sq rt 26 or 35.693 to 3 d.p.
All of the points on a parabola define a parabola. However, the vertex is the point in which the y value is only used for one point on the parabola.
The points of intersection of the equations 4y^2 -3x^2 = 1 and x -2 = 1 are at (0, -1/2) and (-1, -1)
First you need more details about the parabola. Then - if the parabola opens upward - you can assume that the lowest point of the triangle is at the vertex; write an equation for each of the lines in the equilateral triangle. These lines will slope upwards (or downwards) at an angle of 60°; you must convert that to a slope (using the tangent function). Once you have the equation of the lines and the parabola, solve them simultaneously to check at what points they cross. Finally you can use the Pythagorean Theorem to calculate the length.
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
This is a parabola pointing 'down'. It's apex is at the point (4,0). It crosses the x-axis at the points (2,0) and (-2,0)
I'm guessing you mean y = xÂ², which is the equation of a parabola. There is no one answer. Every point which lies on the parabola is the solution set to the equation. Some examples of points which satisfy this are: (0,0) (1,1) (2,4) (-3,9) (-5,25) and (Â½,Â¼)
"From the geometric point of view, the given point is the focus of the parabola and the given line is its directrix. It can be shown that the line of symmetry of the parabola is the line perpendicular to the directrix through the focus. The vertex of the parabola is the point of the parabola that is closest to both the focus and directrix."-http://www.personal.kent.edu/~rmuhamma/Algorithms/MyAlgorithms/parabola.htm"A line perpendicular to the axis of symmetry used in the definition of a parabola. A parabola is defined as follows: For a given point, called the focus, and a given line not through the focus, called the directrix, a parabola is the locus, or set of points, such that the distance to the focus equals the distance to the directrix."-http://www.mathwords.com/d/directrix_parabola.htm
One way would be to graph the two equations: the parabola y = xÂ² + 4x + 3, and the straight line y = 2x + 6. The two points where the straight line intersects the parabola are the solutions. The 2 solution points are (1,8) and (-3,0)
Consider the line segment between the points of (6, 8) and (3, 4) Using Pythagoras' theorem its length is: (6-3)squared+(8-4)squared = 25 So the square root of 25 is 5 which is the length of the line
If: y = x2+4 and y = 5x+10 Then: x2+4 = 5x+10 And: x2-5x-6 = 0 Solving the above quadratic equation: x = -1 or 6 So: when x = -1 then y = 5 and when x = 6 then y = 40 Points of intersection: (-1, 5) and (6, 40) Length of line: the square root of [(6--1)2+(40-5)2] = 35.693 to 3 d.p.
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)
To graph a parabola you must find the axis of symmetry, determine the focal distance and write the focal as a point, and find the directrix. These are all the main points you need to be able to draw a parabola.