Quadratic Transformations

Front

What is the vertex form of a quadratic function?

Back

f(x) = a(x-h)² + k

Front

What transformation occurs when changing y = x² to y = (x - 4)²?

Back

Shifted right 4 units

Front

What transformations occur when changing y = x² to y = -1/2(x-4)² + 1?

Back

Reflected across x-axis, compressed by 1/2, shifted 4 units right and 1 unit up

Front

Match the equation to its description: y = -x² + 4

Back

Reflected over x-axis and shifted up 4

Front

If f(x) = x², what is g(x) if g(x) = f(x) - 5?

Back

g(x) = x² - 5

Front

What does the 'a' in the vertex form f(x) = a(x-h)² + k represent?

Back

The vertical stretch or compression factor; if |a| > 1, the graph is stretched; if 0 < |a| < 1, it is compressed.

Front

What does the 'h' in the vertex form f(x) = a(x-h)² + k represent?

Back

The horizontal shift of the graph; if h is positive, the graph shifts to the right; if negative, it shifts to the left.

Front

What does the 'k' in the vertex form f(x) = a(x-h)² + k represent?

Back

The vertical shift of the graph; if k is positive, the graph shifts up; if negative, it shifts down.

Front

How does the graph of y = -x² compare to y = x²?

Back

It is reflected over the x-axis.

Front

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

Back

It reflects the graph over the x-axis.