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The graph of the function y=x^(2) is shown. How will the graph change if the equation is changed to y=(1//4)x^(2) ? The parabola will become narrower. The parabola will move up 1//4 unit. The parabola will become wider. The parabola will move down 1//4 unit.

The graph of the function y=x2 y=x^{2} is shown. How will the graph change if the equation is changed to y=(1/4)x2 y=(1 / 4) x^{2} ?\newlineThe parabola will become narrower.\newlineThe parabola will move up 1/4 1 / 4 unit.\newlineThe parabola will become wider.\newlineThe parabola will move down 1/4 1 / 4 unit.

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Q. The graph of the function y=x2 y=x^{2} is shown. How will the graph change if the equation is changed to y=(1/4)x2 y=(1 / 4) x^{2} ?\newlineThe parabola will become narrower.\newlineThe parabola will move up 1/4 1 / 4 unit.\newlineThe parabola will become wider.\newlineThe parabola will move down 1/4 1 / 4 unit.
  1. Compare Equations: Compare the two equations y=x2y = x^2 and y=(14)x2y = (\frac{1}{4})x^2 to determine the effect of the coefficient on the x2x^2 term.\newlineThe original equation y=x2y = x^2 has a coefficient of 11 on the x2x^2 term, which means the parabola opens upwards and is of standard width.\newlineThe new equation y=(14)x2y = (\frac{1}{4})x^2 has a coefficient of 14\frac{1}{4} on the x2x^2 term, which is less than 11. This coefficient will affect the width of the parabola.
  2. Effect of Coefficient: Analyze the effect of the coefficient (14)(\frac{1}{4}) on the width of the parabola. A coefficient less than 11 (but greater than 00) on the x2x^2 term will cause the parabola to become wider compared to the parabola with a coefficient of 11. This is because the yy values increase more slowly as xx moves away from the vertex, causing the parabola to spread out more.
  3. Analysis of Width: Determine if there is any vertical shift in the parabola due to the change in the equation.\newlineSince there is no constant term added or subtracted from the equation, there is no vertical shift in the parabola. The vertex remains at the origin (0,0)(0,0).
  4. Vertical Shift: Conclude the effect of changing the equation from y=x2y = x^2 to y=(14)x2y = (\frac{1}{4})x^2. The graph of the function y=(14)x2y = (\frac{1}{4})x^2 will become wider compared to the graph of y=x2y = x^2. There is no vertical shift or narrowing of the parabola.

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