5.3 Transformations of Parabolas Goal : Write a quadratic in Vertex Form and use graphing transformations to easily graph a parabola

The functions in the first column are written in “Vertex Form” What do you notice about the relationship between the Vertex Form and the vertex that you found in the 3 rd column? The functions in the first column are written in “Vertex Form” What do you notice about the relationship between the Vertex Form and the vertex that you found in the 3 rd column?

Vertex Form of a Quadratic Vertex Form of a Quadratic Equation: f(x) = a(x – h) 2 + k Vertex Form of a Quadratic Equation: f(x) = a(x – h) 2 + k Parent Function: y = x 2 Sketch: Vertical reflection if a is negative, vertical stretch (a > 1) or shrink (a < 1) Horizontal translation (opposite of what you see!) Vertical translation *The vertex of the parabola is (h, k) and the axis of symmetry is x = h.

Graphing Equations in Vertex Form xy a. Vertex b. Axis of symmetry c. Table Point Vertex Corresp. d. Ask: Correct reflection? Correct stretch or shrink?

Try this one… a. Vertex b. Axis of symmetry c. Table Point Vertex Corresp. d. Ask: Correct reflection? Correct stretch or shrink? xy

Vertex Form from Graph Ex 4) Write the equation for the following parabola in vertex form: From the graph, write down: Vertex (h, k) Another point (x, y) So we’re solving for a y = a(x – h) 2 + k Do the transformations seem correct?

Vertex Form from Standard Form Ex 5)Write the equation in vertex form. a. Find x-coordinate of vertex (h): b. Find y-coordinate of vertex (k): c. Substitute a, h, and k into vertex form: