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.
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
1 answer
1 answer