Which equation best represents the graph shown below? Explain in detail how you arrived at your answer by stating each of the mathematical transformations necessary to produce the graph on your scratch work.
ik the answer is Y=(X+2)^(2)-3 I just don't know how to solve it
To determine the equation that represents the given graph, it is important to identify the key characteristics and transformations. Start by examining the vertex, direction, and shape of the graph.
From the graph, it can be observed that the vertex appears to be at (-2, -3), indicating a horizontal translation of 2 units to the left and a vertical translation of 3 units downward compared to the basic parabola y = x^2.
So far, the equation can be expressed as y = (x ± h)^2 ± k, where (h, k) represents the vertex.
Next, consider the direction and shape of the graph. Based on the given graph, the parabola opens upwards, suggesting a positive leading coefficient for the squared term.
Hence, the equation can now be optimized to y = (x + 2)^2 - 3, where the vertex is (-2, -3), indicating a transformation of the basic parabola y = x^2 through horizontal and vertical translations.
In summary, the equation that best represents the given graph is y = (x + 2)^2 - 3.
To determine the equation that represents the given graph, we need to analyze the transformations that have been applied to the parent function f(x) = x^2.
The given graph involves the following transformations:
1. Horizontal Shift: The graph has been shifted 2 units to the left, which means we need to subtract 2 from x.
2. Vertical Shift: The graph has been shifted 3 units downward, so we need to subtract 3 from the entire function.
3. Vertical Stretch/Compression: No vertical stretch or compression is evident in the graph, so we don't need to make any adjustments here.
By considering these transformations, we can construct the equation step by step.
Start with the parent function f(x) = x^2:
f(x) = x^2
1. Apply the horizontal shift:
To shift the graph 2 units to the left, subtract 2 from x:
f(x + 2) = (x + 2)^2
2. Apply the vertical shift:
To shift the graph 3 units downward, subtract 3 from the entire function:
f(x + 2) - 3 = (x + 2)^2 - 3
Hence, the equation that represents the given graph is:
y = (x + 2)^2 - 3.