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Transformations of Quadratic Functions

Transformations of Quadratic Functions 1.1 - Solution

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We want to draw the graph of the given function, which has the form y=x2+k,y=x^2+k, where kk is either a positive or a negative number. y=x2+3\begin{gathered} y=x^2+3 \end{gathered} To do so, we will first draw the graph of its parent function, y=x2.y=x^2. Recall that the graph of y=x2y=x^2 is a parabola opening upwards, with vertex (0,0),(0,0), whose axis of symmetry is the vertical line x=0,x=0, and passes through the points (1,1)(1,1) and (-1,1).(\text{-} 1,1).

Our function is a vertical translation of the parent function by 33 units in the positive direction. Thus, we will translate the above graph 33 units upwards.