If: y = x^2 +3x -10 and y = -x^2 -8x -15
Then: x^2 +3x -10 = -x^2 -8x -15
Transposing terms: 2x^2 +11x +5 = 0
Factorizing the above: (2x +1)(x +5) = 0 meaning x = -1/2 or -5
Therefore by substitution points of intersection are at: (-1/2, -45/4) and (-5, 0)
The vertex of this parabola is at -3 -1 When the y-value is 0 the x-value is 4. The coefficient of the squared term in the parabolas equation is 7
The points of intersection of the equations 4y^2 -3x^2 = 1 and x -2 = 1 are at (0, -1/2) and (-1, -1)
xx^(2) + y^(2) = 25 => x^(2) + y^(2) = 5^(2) This is the circle equation, in Cartesian Co-ordinates. It is also the Pythagorean Eq'n.
-2p squared
It is: 2b squared
Points of intersection work out as: (3, 4) and (-1, -2)
They intersect at the point of: (-3/2, 11/4)
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)
The vertex coordinate point of the vertex of the parabola y = 24-6x-3x^2 when plotted on the Cartesian plane is at (-1, 27) which can also be found by completing the square.
It is the Cartesian equation of an ellipse.
The vertex of this parabola is at -3 -1 When the y-value is 0 the x-value is 4. The coefficient of the squared term in the parabolas equation is 7
If: y = 4x2-2x-1 and y = -2x2+3x+5 Then: 4x2-2x-1 = -2x2+3x+5 And so: 6x2-5x-6 = 0 Using the the quadratic equation formula: x = -2/3 and x = 3/2 Substitution: when x = -2/3 then y = 19/9 and when x = 3/2 then y = 5 Points of intersection: (-2/3, 19/9) and (3/2, 5)
The points of intersection are: (7/3, 1/3) and (3, 1)
A parabola is a type of graph that is not linear, and mostly curved. A parabola has the "x squared" sign in it's equation. A parabola is not only curved, but all the symmetrical. The symmetrical point, the middle of the parabola is called the vertex. You can graph this graph with the vertex, x-intercepts and a y-intercept. A parabola that has a positive x squared would be a smile parabola, and the one with the negative x squared would be a frown parabola. Also, there are the parabolas that are not up or down, but sideways Those parabolas have x=y squared, instead of y = x squared.
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)
You need two, or more, curves for points of intersection.
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