In Exercises 27-42, a) Write the equation in the form...

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Key Concepts

Graphing Parabolas

Graphing parabolas involves plotting the vertex, determining the axis of symmetry, and using the coefficient a to understand the parabola’s direction and openness. When the equation is written in vertex form, it becomes much easier to assess these features and accurately sketch the graph, including the consideration of whether it opens upward, downward, left, or right.

Vertex Form of a Parabola

The vertex form of a parabola's equation, whether in the form y = a(x-h)² + k for vertical parabolas or x = a(y-k)² + h for horizontal parabolas, directly reveals the vertex of the parabola and makes identifying its orientation, direction, and width straightforward.

Completing the Square

Completing the square is a method used to convert a quadratic expression into a perfect square plus a constant. This process simplifies the quadratic, making it easier to reformat the equation into vertex form, which is essential for analyzing the properties of the parabola.

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