translations of quadratic functions

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the parent function of quadratic functions?

Back

The parent function of quadratic functions is f(x) = x².

Front

How does the graph of a quadratic function look?

Back

The graph of a quadratic function is a parabola, which opens upwards if a > 0 and downwards if a < 0.

Front

What does it mean to translate a function?

Back

To translate a function means to shift its graph horizontally or vertically without changing its shape.

Front

What is the effect of translating a quadratic function left or right?

Back

Translating a quadratic function left or right involves changing the x-value in the function's equation. For example, f(x + h) translates left by h units.

Front

What is the effect of translating a quadratic function up or down?

Back

Translating a quadratic function up or down involves adding or subtracting a constant from the function's output. For example, f(x) + k translates up by k units.

Front

If f(x) = x², what is g(x) if it is translated down 4 units?

Back

g(x) = f(x) - 4 = x² - 4.

Front

If f(x) = x², what is g(x) if it is translated left 4 units?

Back

g(x) = f(x + 4) = (x + 4)².

Front

What is the transformation of g(x) = (x - 5)² compared to f(x) = x²?

Back

g(x) is translated right 5 units compared to f(x).

Front

What is the transformation of g(x) = x² + 5 compared to f(x) = x²?

Back

g(x) is translated up 5 units compared to f(x).