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Algebra 2 – Parabola – Direction and Vertex










































Parabola

   • In which direction does the parabola given by the equation below open?

           y = -3(x + 4)² + 6

   • What is the vertex of the parabola given by the equation below?

           x = -4(y - 3)² + 2

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Sep 25, 2012
Parabola – Direction and Vertex
by: Staff


Answer:


   • In which direction does the parabola given by the equation below open?


           y = -3(x + 4)² + 6

       The parabola opens downward.

       The minus sign at the beginning of the equation shows that the parabola opens downward.


Math – Parabola – Vertex (-4,6)



   • What is the vertex of the parabola given by the equation below?
           x = -4(y - 3)² + 2

       The vertex of the parabola is (2,3).

       You can solve for the y value of the vertex as follows:

           -4(y - 3)² = 0

           -4(y - 3)² / (-4) = 0 / (-4)

           -4(y - 3)² / (-4) = 0

           (y - 3)² * [(-4) / (-4)] = 0

           (y - 3)² * 1 = 0

           (y - 3)² = 0

           (y - 3)² = 0

           √[(y - 3)²] = √0

           (y - 3) = 0

           y - 3 = 0

           y - 3 + 3 = 0 + 3

           y + 0 = 0 + 3

           y = 3



       You can solve for the x value of the vertex as follows:

           x = -4(y - 3)² + 2

           let y = 3 (the y coordinate of the vertex)

           x = -4(3 - 3)² + 2

           x = -4(0)² + 2

           x = 0 + 2

           x = 2


Math – Parabola – Vertex (2,3)



Thanks for writing.

Staff
www.solving-math-problems.com



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