How many parameters in a quadratic function in a vertex form change when you change the location of the vertex?
( P and Q change? The value of the coefficient( a ) may also change?)
a does not change
y-k = a(x-h)
has vertex at (h,k) regardless of a.
Thank you
In a quadratic function written in vertex form, the general expression is (y - k) = a(x - h)^2, where (h, k) represents the coordinates of the vertex. Changing the location of the vertex indeed affects the parameters in the function.
When you change the location of the vertex, the parameter "h" (representing the x-coordinate of the vertex) changes. If you move the vertex horizontally left or right, "h" will be a different value.
Likewise, the parameter "k" (representing the y-coordinate of the vertex) changes when you change the location of the vertex vertically up or down. A different location for the vertex will result in a different value for "k".
On the other hand, the coefficient "a" in the function does not directly change when you shift the vertex. The coefficient "a" determines the steepness of the curve and whether the parabola is facing upward or downward. However, when you change the vertex, it might indirectly affect the value of "a" if the parabola needs to be stretched or compressed to accommodate the new vertex position.
To summarize, when you change the location of the vertex in a quadratic function in vertex form:
- The parameter "h" (x-coordinate of the vertex) changes.
- The parameter "k" (y-coordinate of the vertex) changes.
- The coefficient "a" (determining the steepness and orientation) may also change indirectly depending on the new vertex position.