How do figure out if a porabala is streched or compressed?
To determine if a parabola is stretched or compressed, you need to examine its equation and compare it to the standard form of a parabola.
The standard form of a parabola is given by the equation y = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola. The parameter "a" in the equation determines the stretch or compression of the parabola.
If the value of "a" is greater than 1, the parabola will be vertically stretched. This means that the graph will be taller and narrower compared to the standard form. On the other hand, if the value of "a" is between 0 and 1, the parabola will be vertically compressed. This results in a graph that is shorter and wider than the standard form.
For example:
1. Suppose you have the equation y = 2(x - 3)^2 + 1. In this case, "a" is equal to 2, which is greater than 1. Therefore, the parabola is vertically stretched.
2. Consider the equation y = 0.5(x + 1)^2 - 2. Here, "a" is 0.5, which is between 0 and 1. Hence, the parabola is vertically compressed.
By analyzing the value of "a" in the equation, you can determine whether the parabola is stretched or compressed compared to the standard form.