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Foundations

Graphing a Quadratic

To sketch the graph of a quadratic equation, follow these steps:
  • Find a, b, and c of the equation.
  • Check if a > 0 or a < 0 to decide if the graph opens up (a > 0) or down (a < 0).
  • Find the vertex. This is the minimum or maximum point of the parabola. The x-coordinate can be found by the equation GraphQuad . Once found, substitute this value into the original equation to find the value of y. These will be the (x,y) coordinates of the vertex.
  • Find the y-intercept by substituting 0 in for x in the equation.
  • Find the x-intercepts by substituting y = 0 and solving the quadratic equation. Use either the quadratic formula, completing the square, or put the equation in factored form to solve for x.