Writing Equations and Putting It All Together

This final page combines all the concepts learned to write equations based on described transformations.

Key points about the vertex form y = a(x - h)² + k:

• h represents the horizontal shift (positive h shifts left, negative h shifts right)
• k represents the vertical shift (positive k shifts up, negative k shifts down)
• If a is negative, the function is reflected over the x-axis
• |a| > 1 represents a vertical stretch, while 0 < |a| < 1 represents a vertical compression

The page includes practice problems for writing equations based on described transformations from the parent function.

Example: A function translated 3 units left and 4 units down can be represented as y = (x + 3)² - 4.

Highlight: Being able to write equations based on described transformations demonstrates a deep understanding of how the coefficients and constants in a quadratic equation affect its graph.

Vocabulary: Vertical stretch occurs when |a| > 1, while vertical compression occurs when 0 < |a| < 1 in the vertex form of a quadratic equation.