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Transformations of Quadratic Functions

Transformations of Quadratic Functions 1.7 - Solution

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We want to draw the graph of the given quadratic function, which has the form y=(xh)2,y=(x-h)^2, where hh is either a positive or a negative number. y=(x+5)2y=(x(-5))2\begin{gathered} y=(x+5)^2 \quad \Leftrightarrow \quad y=\big(x-(\text{-} 5)\big)^2 \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 passing through the points (1,1)(1,1) and (-1,1).(\text{-} 1,1).

Our function is a horizontal translation of the parent function by 55 units in the negative direction. Thus, we will translate the above graph 55 units to the left.