Quadratic Relationships

Graphing Vertex Form

Learning Goals

  1. Understand how to graph a parabola using an equation
  2. How to graph using transformation
  3. Label parts of a parabola
  4. Different ways to graph a parabola
  5. How to find the value of (a), (h) and (k) in an equation

Definitions:

Parabola- A two-dimensional, symmetrical curve, that is often shown on a graph

Vertex Form- An equation that uses values of a, h and k to determine the vertex and plot the x and y-intercepts

Summary

  • Vertex (h,k): Axis of symmetry (x=h) and Optimal value (y=k)
  • (a) tells you the direction of opening and compression or stretch (in front of the equation)
  • (h) horizontal translation (inside the bracket before it is closed)
  • (k) vertical translation (the final value at the end of the equation)
  • step pattern (a multiplied by 1, 3 and 5)
  • to find the y-intercept, set x=0 and solve for y
  • to solve, set y=0 and solve for x or expand and simplify to get the standard form, then use the quadratic formula

Graph

Parabola in Vertex Form

  • y = (x - h)^2 + k form
  • Positive Parabola (value of a is positive)
  • 3 units to the right (h value is -3 which becomes positive)
  • 2 units high (k value is 2)
  • Vertex is (h, k)
Big image
Vertex Form word problem
Graphing Using Transformations