Quadratic Transformations Mixed

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 of the parabola.

Front

What effect does the 'a' value have in the vertex form of a quadratic function?

Back

The 'a' value determines the vertical stretch or compression of the parabola. If |a| > 1, the parabola is narrower; if 0 < |a| < 1, it is wider.

Front

How does a negative 'a' value affect the graph of a quadratic function?

Back

A negative 'a' value reflects the parabola over the x-axis.

Front

What does translating a quadratic function to the right by 'h' units look like in vertex form?

Back

To translate right by 'h' units, the function becomes f(x) = a(x - h)² + k.

Front

What does translating a quadratic function up by 'k' units look like in vertex form?

Back

To translate up by 'k' units, the function becomes f(x) = a(x - h)² + k.

Front

What is the parent function of a quadratic equation?

Back

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

Front

How do you represent a vertical compression of a quadratic function?

Back

A vertical compression is represented by a value of 'a' between 0 and 1 in the vertex form f(x) = a(x - h)² + k.

Front

What is the effect of moving a quadratic function 3 units left and 4 units up?

Back

The function becomes f(x) = (x + 3)² + 4.

Front

How do you find the equation of a parabola that has been stretched by a factor of 2 and moved 5 units to the right and 3 units down?

Back

The equation is f(x) = 2(x - 5)² - 3.

Front

What does a vertical stretch of a quadratic function look like?

Back

A vertical stretch occurs when 'a' is greater than 1 in the vertex form f(x) = a(x - h)² + k.