Vertex Determination

The vertex of the equation can be determined by finding an equation for the graph in the form y = a(x+b)^2+c. This was done by using the Completing The Squares Method of factoring:

y = 2x^2 + 3x - 4 becomes

y = 2x^2 + 3x + (9/8) - (41/8)

y = 2 (x + 3/4)^2 - (41/8)

This new form of the equation can be used to find the vertex, using the knowledge that the vertex will occur at x = -b.

For this equation, -b = -3/4, so the vertex is (-3/4 , -41/8)

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