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How to Tell Which Direction a Parabola Will Be Graphed

Quadratic equations have a general form of y=ax^2 + bx + c and graph as a U shape called a parabola. A parabola can be wide or narrow and face up or down. The highest point of an upside-down parabola, or the lowest point of a right-side-up parabola, is called the vertex, represented by point (h, k). The vertex is found using the information from the general form plugged into the formula h = -b/2a. The answer is plugged back in the general form in place of x and the equation is solved for y. The result is the k in the point (h, k).

Instructions

- 1
  Determine what direction a parabola will be graphed by examining the general form of the equation: y = ax^2 + bx + c. Note that if the a, called the leading coefficient, is positive, the parabola will face up and if it's negative, the parabola will face down.
- 2
  Determine the direction and the vertex for the quadratic equation y = 6x^2 + 2y + 4. Write that the parabola will face up since the leading coefficient is a positive 6 and because of this direction, the vertex will form its lowest point.
- 3
  Plug the known information into the vertex formula h = -b/2a: h = -2/(2 * 6) = -2/12 = -1/6. Plug this answer in for the x variables in the general form: 6(-1/6)^2 + 2(-1/6) + 4 = (6/36) - (2/6) + 4. Convert the fractions to perform the operations: (1/6) - (2/6) + (24/6) = (23/6) = 3.8 (rounded). Write that the vertex point is (-1/6, 3.8) or (-0.2, 3.8).

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