How is the graph of $y = - \frac{1}{3} x^{2} - 4$ $y=-1/3x^2-4$ related to the graph of $f (x) = x^{2}$ $f(x)=x^2$ ?

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How is the graph of $y = - \frac{1}{3} x^{2} - 4$ $y=-1/3x^2-4$ related to the graph of $f (x) = x^{2}$ $f(x)=x^2$ ?

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Answer 1 · 2017-02-17T16:31:52

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Explanation:

$1 \to$ $color(blue)(1->)$ The general shape of the graph $y = x^{2}$ $y=x^2$ is that of $\cup$ $uu$

$2 \to$ $color(blue)(2->)$ The -4 lowers the graph of $y = x^{2}$ $y=x^2$ by 4

$3 \to$ $color(blue)(3->)$ Putting a minus sign in front of the $x^{2}$ $x^2$ so that we have $y = - x^{2} - 4$ $y=-x^2-4$ turns the whole thing upside. Now we have the general shape $\cap$ $nn$

$4 \to$ $color(blue)(4->)$ the $\frac{1}{3}$ $1/3$ in $y = - \frac{1}{3} x - 4$ $y=-1/3x-4$ has the effect of widening the graph

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How is the graph of $y = - \frac{1}{3} x^{2} - 4$ $y=-1/3x^2-4$ related to the graph of $f (x) = x^{2}$ $f(x)=x^2$ ?

1 Answer

Explanation:

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How is the graph of y=-1/3x^2-4y=−13x2−4y=-1/3x^2-4 related to the graph of f(x)=x^2f(x)=x2f(x)=x^2?

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How is the graph of $y = - \frac{1}{3} x^{2} - 4$ $y=-1/3x^2-4$ related to the graph of $f (x) = x^{2}$ $f(x)=x^2$ ?