Describing Parabolas Solutions

• The vertex form of a quadratic equation is written as: $y=a{\left(x–h\right)}^2+k$

• The    vertex    of a parabola is located at the point (h, k).

• The coefficient a determines the    direction    and    width    of a parabola.

• The variables a, h, and k transform a parabola as compared to the parent graph, $y\mathit{=}{x}^2$. When transformations to the parent graph occur:
  •    a    reflects over the x-axis and stretches/compresses (dilates) the graph.
  •    h    translates (shifts) the graph left or right.
  •    k    translates (shifts) the graph up or down.

Example 1

Identify a, h, and k. Name the vertex and the direction of the graph. 

$y=6{\left(x–3\right)}^2–1$

a = 6, h = 3, k = –1

The graph will open upward because a is positive. The vertex is (3, –1).

Example 2

Describe the transformation from the parent function. Explain your reasoning. Graph.