100 points (algebra one) describe and correct the error in comparing the graphs

Mathematics

1 answer:

Pepsi [2]2 years ago

3 0

Answer:

The error made is that the graph of $y=x^{2} +3$ is a vertical translation up by 3, instead of down.

Step-by-step explanation:

Exponential functions, when they are graphed, use the function $f(x)=a(x-h)^{2} +k$ .

In the equation, k expresses how much the graph shifts vertically. In this case, the function shifts vertically up by 3 from the parent function, $y=x^{2}$ . So, the translation is actually 3 units up compared to the graph of $y=x^{2}$ .

Hope this helps and have an amazing day!! ❤

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Which is the standard form of the equation of the parabola that has a vertex of (3, 1) and a directric of x = -2?

vagabundo [1.1K]

Check the picture below. So,the parabola looks like so, notice the distance "p". since the parabola is opening to the right, then "p" is positive, thus is 5.

$\bf \textit{parabola vertex form with focus point distance}\\\\
\begin{array}{llll}
\boxed{(y-{{ k}})^2=4{{ p}}(x-{{ h}})} \\\\
(x-{{ h}})^2=4{{ p}}(y-{{ k}}) \\
\end{array}
\qquad 
\begin{array}{llll}
vertex\ ({{ h}},{{ k}})\\\\
{{ p}}=\textit{distance from vertex to }\\
\qquad \textit{ focus or directrix}
\end{array}\\\\$

$\bf -------------------------------\\\\
\begin{cases}
h=3\\
k=1\\
p=5
\end{cases}\implies (y-1)^2=4(5)(x-3)\implies (y-1)^2=20(x-3)
\\\\\\
\cfrac{1}{20}(y-1)^2=x-3\implies \boxed{\cfrac{1}{20}(y-1)^2+3=x}$