Algebra 2: Graphing Parabolas Vertex Form

Quadratic Formula in Vertex Form

• The quadratic formula in vertex form is expressed as y = a(x-h)² + k.

Components of the Vertex Form

• "a" indicates the slope to the point one unit from the vertex, determining the width and direction of the parabola.
• "h" represents the x-coordinate of the vertex and defines the axis of symmetry of the parabola.
• "k" denotes the y-coordinate of the vertex, providing the vertical position of the parabola's turning point.

Vertex

• The vertex of the parabola can be found at the coordinates (h, k).

Axis of Symmetry

• The axis of symmetry is located at h, which is a vertical line that divides the parabola into two mirror-image halves.

Slope and Points

• To find the slope to a point one unit from the vertex, use the value of a.

Y-Intercept Calculation

• The y-intercept can be determined by substituting 0 for x in the vertex form equation and solving for y.

Standard Form Comparison

• The standard form of a quadratic equation is represented as y = ax² + bx + c.

Min/Max Characteristics

• If a is positive, the vertex indicates a minimum point on the graph.
• If a is negative, the vertex indicates a maximum point on the graph.

Graphing Information

• To accurately graph a parabola in vertex form, identify the following:
  • Axis of symmetry
  • Vertex
  • Slope to a point one unit from the vertex
  • Y-intercept