Introduction to Parabola Transformations
The simplest quadratic function is f = x², which creates a U-shaped curve called a parabola with its vertex at (0,0). This basic parabola serves as our starting point before applying any transformations.
You can change this basic parabola's position, size, and orientation through different transformations. When moving a parabola horizontally, we use f or f — if h is positive, the graph shifts right; if h is negative, it shifts left. For vertical movements, we use f + k or f - k — positive k moves the graph up, while negative k moves it down.
Reflection is another key transformation that flips the parabola. When you write -f, you're reflecting the parabola about the x-axis, turning the U-shape upside-down into an upside-down U.
💡 Think of transformations like dressing up your parabola! Horizontal shifts move it side to side, vertical shifts move it up and down, and reflections flip it over like a pancake.
