Quadratic transformations

Front

What is the parent function of a quadratic equation?

Back

The parent function of a quadratic equation is y = x².

Front

How does the value of 'a' in the function y = a(x-h)² + k affect the graph?

Back

If 'a' is greater than 1, the graph is narrower; if 'a' is between 0 and 1, the graph is wider.

Front

What does the vertex form of a quadratic function look like?

Back

The vertex form is f(x) = a(x-h)² + k, where (h,k) is the vertex.

Front

What is the effect of a positive 'k' in the vertex form of a quadratic function?

Back

A positive 'k' results in a vertical shift of the graph upwards.

Front

What is the effect of a negative 'k' in the vertex form of a quadratic function?

Back

A negative 'k' results in a vertical shift of the graph downwards.

Front

How do you find the vertex of the function f(x) = 5(x+6)² - 7?

Back

The vertex is (-6, -7).

Front

What transformation does g(x) = (x-3)² represent compared to f(x) = x²?

Back

It represents a horizontal shift to the right by 3 units.

Front

What transformation does g(x) = (x+3)² represent compared to f(x) = x²?

Back

It represents a horizontal shift to the left by 3 units.

Front

What transformation does g(x) = x² + 5 represent compared to f(x) = x²?

Back

It represents a vertical shift upwards by 5 units.

Front

What transformation does g(x) = x² - 5 represent compared to f(x) = x²?

Back

It represents a vertical shift downwards by 5 units.