2.1 Transformations of Quadratic Functions

Front

What is the parent function of a quadratic function?

Back

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

Front

How does the coefficient of x² affect the width of the parabola?

Back

If the coefficient is greater than 1, the parabola is narrower; if it is between 0 and 1, the parabola is wider.

Front

What is the vertex form of a quadratic function?

Back

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

Front

How do you identify the vertex from the vertex form of a quadratic function?

Back

The vertex is given by the point (h, k) in the vertex form f(x) = a(x - h)² + k.

Front

What transformation does the equation y = (x - 4)² represent?

Back

It represents a shift to the right by 4 units.

Front

What does a negative coefficient in front of the quadratic term indicate about the parabola?

Back

It indicates that the parabola opens downwards.

Front

What is the effect of adding a constant outside the squared term in the vertex form?

Back

It shifts the graph vertically; adding moves it up, while subtracting moves it down.

Front

If f(x) = x², what is g(x) if g(x) = f(x) + 3?

Back

g(x) = x² + 3, which shifts the graph of f(x) up by 3 units.

Front

What does the transformation y = 3(x - 3)² + 3 indicate?

Back

It indicates a vertical stretch by a factor of 3, a shift right by 3 units, and a shift up by 3 units.

Front

How do you determine if a parabola is wider or narrower than the parent function?

Back

Compare the coefficient of x²: if |a| > 1, it's narrower; if 0 < |a| < 1, it's wider.