A parabola has a vertex located at (6,-5) and passes through the point (8,3). Use the pattern of the parabola to look for a vertical or horizontal stretch. Write the equation of the graph in vertex form.

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Understand Vertex Form: First, we need to understand that the vertex form of a parabola is given by y = a(x-h)^2 + k, where (h,k) is the vertex of the parabola. We are given the vertex (6,-5), so we can substitute h and k into the equation.Substitute Vertex: Substituting the vertex into the vertex form equation, we get y = a(x-6)^2 - 5. Now, we need to find the value of 'a' using the point (8,3) that lies on the parabola.Find Value of 'a': Plugging the point (8,3) into the equation, we get 3 = a(8-6)^2 - 5. Simplifying the right side, we have 3 = a(2)^2 - 5, which simplifies to 3 = 4a - 5.Solve for 'a': To find the value of 'a', we solve the equation 3 = 4a - 5 for 'a'. Adding 5 to both sides gives us 8 = 4a, and dividing both sides by 4 gives us a = 2.Write Final Equation: Now that we have the value of 'a', we can write the final equation of the parabola. Substituting 'a' into the equation y = a(x-6)^2 - 5, we get y = 2(x-6)^2 - 5.

A parabola has a vertex located at $(6,-5)$ and passes through the point $(8,3)$ . Use the pattern of the parabola to look for a vertical or horizontal stretch. Write the equation of the graph in vertex form.

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A parabola has a vertex located at (6,−5) (6,-5) (6,−5) and passes through the point (8,3) (8,3) (8,3). Use the pattern of the parabola to look for a vertical or horizontal stretch. Write the equation of the graph in vertex form.

A parabola has a vertex located at $(6,-5)$ and passes through the point $(8,3)$ . Use the pattern of the parabola to look for a vertical or horizontal stretch. Write the equation of the graph in vertex form.