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Algebra II Recipe: Graphing a Quadratic Equation
A. Definitions
  1. Parabola - the graph of a quadratic equation, which is u-shaped
  2. Vertex Point - it's the highest or lowest point on the graph
  3. Axis of Symmetry - the vertical line that goes through the vertex point
  4. Standard Form - y = ax² + bx + c
  5. Vertex Form - y = a(x - h)² + k
B. Steps for Graphing a Quadratic Equation in Standard Form
  1. Determine if the graph will open up or down.
    • Opens up if "a" is positive (the vertex point will be the minimum point).
    • Opens down if "a" is negative (the vertex point is the maximum point).
  2. Find the vertex point.
    • Find the x-value by x = -b/(2a).
    • Find the y-value by substituting the x-value into the equation and solving for "y".
  3. Find more points to determine the graph.
    • Choose two integers larger than the x-value of the vertex point.
    • Choose two integers smaller than the x-value of the vertex point.
    • Substitute these values in place of "x" in the equation and solve for "y".
    • Four ordered pairs have been found.
  4. Graph and connect all points that have been found.
y = 2x² - 8x + 6
y = -2x² + 8x - 5
C. Graphing a Quadratic Equation in Vertex Form
  1. Determine the vertex point (h,k) and graph it.
  2. Graph the axis of symmetry.
  3. Choose two x-values on the side of the axis of symmetry closest to the origin and determine the points.
  4. Use symmetry to graph the two points on the other side of the axis of symmetry.
  5. Connect the points.
y = (x + 1)² + 4

y = -3(x - 2)² + 5

G Redden

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