3 years ago

On a piece of paper, graph f(x)= {x if x<2 2 if x>2}

Mathematics

1 answer:

r-ruslan [8.4K]3 years ago

4 0

Answer:

see below

Step-by-step explanation:

The graph has two parts. There is one line for x < 2. It has a slope of 1 and a y-intercept of 0.

The line for x > 2 is the horizontal line x=2.

The point at x=2 is not defined by the function you have posted here, so there is a "hole" in the graph at that point.

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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?

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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.

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

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