IB MYP 4-5 Maths- Transformation of quadratic functions- Study Notes - New Syllabus

IB MYP 4-5 Maths- Transformation of quadratic functions – Study Notes

Extended

Transformation of Quadratic Functions

The basic quadratic function is:

\( y = x^2 \)

The general form after transformation is:

\( y = a(x – h)^2 + k \)

Types of Transformations and Their Effect on the Function:

Vertical Shift:
Change: \( y = f(x) + k \)
Effect: Shift up by \( k \) if \( k > 0 \), down by \( |k| \) if \( k < 0 \).
Horizontal Shift:
Change: \( y = f(x – h) \)
Effect: Shift right by \( h \) if \( h > 0 \), left by \( |h| \) if \( h < 0 \).
Vertical Stretch/Compression:
Change: \( y = a \cdot f(x) \)
Effect: If \( |a| > 1 \), parabola is narrower (stretched). If \( 0 < |a| < 1 \), it is wider (compressed).
Reflection in the x-axis:
Change: \( y = -f(x) \)
Effect: Flips the parabola upside down.

Vertex Form: \( y = a(x – h)^2 + k \)

Vertex: \( (h, k) \)

Axis of Symmetry: \( x = h \)

Example :

Describe the transformation of \( y = (x – 3)^2 + 2 \) from \( y = x^2 \).

▶️ Answer/Explanation

Compare with \( y = (x – h)^2 + k \):

New Vertex: (3, 2).

Example :

Describe the transformation of \( y = -2(x + 1)^2 – 4 \) from \( y = x^2 \).

▶️ Answer/Explanation

Compare with \( y = a(x – h)^2 + k \):

New Vertex: (-1, -4).

Summary Table of Transformation