Summary of 3 forms of quadratic function NOTE

Summary of 3 forms of quadratic function NOTE: The “a” in each form is EXACTLY the same number. It is the only value that CHANGES the SHAPE of the curve. It is the only non-rigid transformation. The other numbers change the location of the curve. They are all RIGID transformations.

Common for all 3 forms: Standard: f(x) = ax 2 + bx + c Vertex: f(x) = a(x – h)2 + k Intercept: f(x) = a(x – p)(x – q) The “a” in each form is EXACTLY the same number. It is the only value that CHANGES the SHAPE of the curve. It is the only non-rigid transformation. The other numbers change the location of the curve. They are all RIGID transformations.

Standard Form of the Quadratic Stretch Factor y= 2 ax Rigid VERTICAL Shift (y-intercept) + bx + c Axis of Symmetry is: Find “y” part of vertex by substituting the axis of symmetry into the equation for “x” Use the “x” and “y” to change to vertex form Factor to change to intercept form

Vertex Form of the Quadratic (can find the vertex easily at (h, k)) From parent curve of: y = x 2 Stretch factor Rigid Shift VERTICAL amount y = a(x – 2 h) Rigid Shift HORIZONTAL +k amount Distribute to change to standard form

Intercept Form of the Quadratic (can find the intercepts easily) Stretch Factor y = a(x – p)(x – q) The x-intercepts are at (p, 0) and (q, 0) Axis of Symmetry is located in the middle of the intercepts, so it is: Find “y” part of vertex by substituting the axis of symmetry into the equation for “x” Distribute to change to standard form