Use the equation of the parabola in standard form...

Use the equation of the parabola in standard form $y=a(x-h)^{2}+k$ to determine the coordinates of the vertex and the equation of the axis of symmetry (complete the square if necessary). Then graph the parabola.
$$y=(x-1)^{2}+1$$
CAN'T COPY THE GRAPH

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Key Concepts

Vertex Form

The vertex form of a quadratic function is written as y = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola and a determines the shape and direction of its opening. This form makes it straightforward to identify key characteristics of the graph, such as the vertex and the axis of symmetry.

Vertex

The vertex is the point (h, k) in the vertex form of a quadratic equation. It denotes the maximum or minimum point of the parabola, depending on whether it opens downward or upward, respectively.

Axis of Symmetry

The axis of symmetry is the vertical line that runs through the vertex of the parabola, given by the equation x = h. This line divides the parabola into two mirror-image halves.

Completing the Square

Completing the square is a technique used to convert a quadratic equation in standard form into vertex form. This process involves rewriting the quadratic expression as a perfect square trinomial, which makes it easier to identify the vertex and other key graph characteristics.

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