Question

properties of square root graphs

they have a \underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad} \\((h, k)\\), where we change the sign of \underline{\qquad} and keep the sign of \underline{\qquad} the same.

Explanation:

🆕 New Concept Discovered: Square Root Functions
How square root graphs start and shift

Step 1: Identify the starting point of a square root graph

A square root function in its standard vertex (or starting) form is written as:

$$ y = a\sqrt{x - h} + k $$

The point \( (h, k) \) represents the starting point or endpoint of the ray-like curve. In many algebra curricula, this point is referred to as the starting point (or sometimes endpoint or vertex).

Step 2: Determine how to find the coordinates from the equation

When extracting the starting point \( (h, k) \) from the equation \( y = a\sqrt{x - h} + k \):

• Inside the square root, we have \( x - h \). To find the \( x \)-coordinate of the starting point, we must change the sign of the value inside, which corresponds to \( h \).
• Outside the square root, we have \( + k \). To find the \( y \)-coordinate of the starting point, we keep the sign of \( k \) the same.

Answer:

They have a starting point (or endpoint) \( (h, k) \), where we change the sign of \( h \) and keep the sign of \( k \) the same.