The graph of a quadratic function is given. Write the...

The graph of a quadratic function is given. Write the function's equation, selecting from the following options.
$$
\begin{array}{ll}
{f(x)=(x+1)^{2}-1} & {g(x)=(x+1)^{2}+1} \\
{h(x)=(x-1)^{2}+1} & {j(x)=(x-1)^{2}-1}
\end{array}
$$
(Graph can't copy)

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Key Concepts

Interpreting Graphical Information

Interpreting a graph involves identifying key features such as the vertex, axis of symmetry, and the direction in which the parabola opens. These elements can then be matched with the corresponding terms in the vertex form of a quadratic function to determine the correct equation.

Graph Transformations

Graph transformations involve shifting, stretching, compressing, or reflecting the graph of a function. In the context of quadratic functions, translations indicated by the terms (x - h) and the constant k move the graph horizontally and vertically, respectively, which helps in matching the equation to its graph.

Vertex Form

The vertex form of a quadratic function is given by a(x - h)² + k, where (h, k) represents the vertex of the parabola. This form makes it easy to graph the function and understand how it is shifted from the origin, as it directly shows the horizontal and vertical translations.

Quadratic Functions

Quadratic functions are second-degree polynomial functions, typically represented in the standard form ax² + bx + c, and are known for their parabolic graphs. They exhibit key properties such as a vertex, an axis of symmetry, and can open upward or downward depending on the sign of the coefficient a.

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