–8(–7r – 7) + 8 =-272

Mathematics

1 answer:

Mademuasel [1]2 years ago

6 0

Answer:

-8(-7r-7)+8=-272

We move all terms to the left:

-8(-7r-7)+8-(-272)=0

We add all the numbers together, and all the variables

-8(-7r-7)+280=0

We multiply parentheses

56r+56+280=0

We add all the numbers together, and all the variables

56r+336=0

We move all terms containing r to the left, all other terms to the right

56r=-336

r=-336/56

r=-6

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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.

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

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