Shannon G.
asked • 07/26/22help me find the midpoint
Vertex C is the midpoint of the vertices (each vertex) for the parabolas given by y = -5(x+4)^2 - 10 and y = 3/2(x+14)(x+10)
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2 Answers By Expert Tutors
Doug C. answered • 07/26/22
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Shannon G.
thank you so much this is so helpful!
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07/26/22
Shannon G.
do u by chance know how to solve and find the area of three vertexes?
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07/26/22
Doug C.
Which 3 vertices? The discovered midpoint is not a vertex.
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07/26/22
Shannon G.
yes Ive got 3 vertexes and its asking me to solve them and then determine the area
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07/26/22
Doug C.
So this is a separate problem? Find the 3 vertices for 3 separate parabolas, then find the area of the triangle formed by those 3 vertices? Finding the area of the triangle will depend on the coordinates. If it is a right triangle (two of the sides are perpendicular), then it will be easy. You will have to find the lengths of the legs using the distance formula. If not a right triangle, you likely will have to find the lengths of at least two of the sides. If this is about right, perhaps sending another question will be appropriate.
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07/26/22
Shannon G.
the question is: Vertex A is the point of intersection of x-2y+16=0 and x+3y-34=0 Vertex B is the vertex of the quadratic relation given by y=-0.5x^2+12x-70 Vertex C is the midpoint of the vertices (each vertex) for the parabolas given by y=-5(x+4)^2-10 and y=3/2(x+14)(x+10) Find vertex A,B,C Graph or Sketch ∆ABC Solve ∆ABC (Calculate all the side lengths and all the angles). Determine the area of ∆ABC.
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07/26/22
Shannon G.
im stuck on the graphing solving and finding area
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07/26/22
Shannon G.
the vertexes I got are A: (4,10) B: (12, 2) and C: (-8,-8)
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07/26/22
Doug C.
Ahh, OK, cool problem. Will give you something shortly.
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07/26/22
Doug C.
Here is a Desmos graph showing the results. The assumption has been made that you are familiar with Law of Sines and Law of Cosines. desmos.com/calculator/jpdrchbtes Your vertices are correct! Take a look at the content of the graph (select and right click on the link above and choose "Go to..." to visit the graph. Look over the steps and decide if you have any questions.
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07/26/22
Doug C.
FYI, here is an updated graph with a folder that finds the equation of the circumcircle for the given triangle. desmos.com/calculator/ait4q1rk6v You might want to look it over to get acquainted with the power of Desmos.
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07/27/22
The vertex is point at the "bottom" of a parabola that points up or the "top" of a parabola that points down.
Your parabola y=-5(x+4)^2-10 is actually written in vertex form. To find the vertex, set (x+4) equal to 0 and solve x+4=0 for x. That's the x-coordinate of the vertex. From there, plug in that value and solve for y.
The other equation, y=3/2(x+14)(x+10), is in factored form. If we set (x+14)=0 and (x+10)=0 and solve for x twice, then we find the two points where the parabola crosses the x-axis. Their midpoint has the x-coordinate of the vertex. From there, plug in and solve for y.
Shannon G.
I don't quite understand, can you show me without the words?
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07/26/22
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Mark M.
Link is broken.07/26/22