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Parabola Y X2 Change

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The shape of the basis parabola y=x2 changes for different forms of the parabolic function causing it to translate, reflect or dilate. Dilation (widening or narrowing) of the parabola occurs when the basis parabola y=x2 is multiplied or divided (m) therefore changing the equation to either y=mx2 or y=x^2/m. For instance, if the parabola is multiplied by two the parabola becomes narrower whereas if the parabola is divided by two the parabola becomes wider. This is evident in the graph in question 1b as when the basis parabola is multiplied by fourteen the parabola becomes narrower however when the basis parabola is divided by fourteen it becomes wider. Reflection of the parabola occurs when the basis parabola y=x2 is changed to y=-x2. For example, …show more content…

Vertical (upwards or downwards) translation of the parabola occurs when the basis parabola y=x2, y-value of each point is increased or decreased therefore changing the equation to either to y=x2+h or y=x2-h. For instance, in order to translate the parabola upwards by 5 units it shifts the general point (a, a2) to (a, a2+5) therefore making the equation, y= x2+5. The vertex of this parabola is now (0,5) but it still has the same axis of symmetry. Likewise, when the basis parabola becomes y=x2-5 the parabola is translated 5 units down with the vertex (0,-5). This can be seen through the graph in question 1a as the parabolas are vertically translated upwards or downwards by using the addition or subtraction of fourteen. Conversely, horizontal translation of the parabola occurs when the translation parabola equation y=x2±h is changed to y=(x±h)2. Therefore, the horizontal translation for the parabola is changed by the value of the variable h, that is subtracted from x before the squaring operation. For example, in order to translate the parabola to the left by 4 units it shifts the general point (a, a2) to (a, (a+2)2) therefore making the equation, y= (x+2)2. The vertex of this parabola is now (0,4). Likewise, when the basis parabola becomes y=(x-2)2 the parabola is translated 2 units to the right with the vertex (0,-4). This can be seen through the graph in

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