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

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Write a quadratic function in vertex form

Full solution

Q. 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}

?

\newline

The parabola will become narrower.

\newline

The parabola will move up

1 / 4

unit.

\newline

The parabola will become wider.

\newline

The parabola will move down

1 / 4

unit.

Compare Equations: Compare the two equations $y = x^2$ and $y = (\frac{1}{4})x^2$ to determine the effect of the coefficient on the $x^2$ term. $\newline$ The original equation $y = x^2$ has a coefficient of $1$ on the $x^2$ term, which means the parabola opens upwards and is of standard width. $\newline$ The new equation $y = (\frac{1}{4})x^2$ has a coefficient of $\frac{1}{4}$ on the $x^2$ term, which is less than $1$ . This coefficient will affect the width of the parabola.
Effect of Coefficient: Analyze the effect of the coefficient $(\frac{1}{4})$ on the width of the parabola. A coefficient less than $1$ (but greater than $0$ ) on the $x^2$ term will cause the parabola to become wider compared to the parabola with a coefficient of $1$ . This is because the $y$ values increase more slowly as $x$ moves away from the vertex, causing the parabola to spread out more.
Analysis of Width: Determine if there is any vertical shift in the parabola due to the change in the equation. $\newline$ Since 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 $(0,0)$ .
Vertical Shift: Conclude the effect of changing the equation from $y = x^2$ to $y = (\frac{1}{4})x^2$ . The graph of the function $y = (\frac{1}{4})x^2$ will become wider compared to the graph of $y = x^2$ . There is no vertical shift or narrowing of the parabola.

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