Square Root Graphs

Front

What is the general form of a square root function?

Back

y = √(x - h) + k, where (h, k) is the vertex of the graph.

Front

What effect does the negative sign in front of a square root function have on its graph?

Back

It reflects the graph across the x-axis.

Front

How does the value of 'h' in the function y = √(x - h) affect the graph?

Back

It shifts the graph horizontally to the right by 'h' units.

Front

What does the value of 'k' in the function y = √(x - h) + k do to the graph?

Back

It shifts the graph vertically upwards by 'k' units.

Front

What is the vertex of the graph of the function y = √(x - 1) + 4?

Back

The vertex is at the point (1, 4).

Front

How does the coefficient in front of the square root function affect the graph?

Back

It stretches or compresses the graph vertically. A value greater than 1 stretches it, while a value between 0 and 1 compresses it.

Front

What is the domain of the function y = √(x + 1)?

Back

The domain is x ≥ -1.

Front

What is the range of the function y = √(x - 4)?

Back

The range is y ≥ 0.

Front

What does the graph of y = 2√(x) look like compared to y = √(x)?

Back

y = 2√(x) is vertically stretched compared to y = √(x).

Front

What is the effect of adding a constant to the square root function, such as in y = √(x) + 3?

Back

It shifts the graph vertically upwards by 3 units.