Example Card: Translating the Vertex
Translate the vertex of a parabola in Grade 9 algebra. Shift parabolas horizontally and vertically using vertex form y=a(x-h)²+k and identify how h and k control the movement.
Key Concepts
The first key idea in this lesson is translating graphs. Let's see how we can move our V shape around the coordinate plane without making a table.
Example Problem.
Graph the function $f(x) = |x 2| + 3$ and give the coordinates of the vertex.
Common Questions
How do you translate a parabola horizontally and vertically?
In vertex form y = a(x - h)² + k, h shifts the parabola horizontally (right for positive h, left for negative), and k shifts vertically (up for positive k, down for negative).
What is the vertex of a parabola in vertex form?
The vertex is the point (h, k) in y = a(x - h)² + k. It is the minimum point when a > 0 (opens up) or maximum point when a < 0 (opens down).
Why does x - h shift the parabola right when h is positive?
The vertex occurs where x - h = 0, i.e., x = h. So h = 3 means the vertex is at x = 3, shifted right 3 units from the origin.