HELP !!!! what is the coordinate of the vertex of the following parabola: -8(x-5)=(y+1)^2
a. (-5, 1)
b. (5, -1)
c. (5, 1)
d. (-8, 1)
Answers
what is the coordinate of the vertex for the following parabola:
-8 ( x - 5 ) = ( y + 1 ) ² (5, -1)
what is the coordinate of the focus for the following parabola:
-8 ( x - 5 ) = ( y + 1 ) ² (3, -1)
The vertex of the equation of a parabola [tex]- 8 (x - 5) = (y + 1)^2[/tex] by compared with the standard form of the equation of a parabola [tex]x = a (y - k)^2 + h[/tex] is,
⇒ (h, k) = (5, - 1)
Where, [tex](h, k)[/tex] is the vertex of the parabola.
We have to give that,
The equation of a parabola is,
[tex]- 8 (x - 5) = (y + 1)^2[/tex]
The standard form of the equation of a parabola is,
[tex]x = a (y - k)^2 + h[/tex]
Where, [tex](h, k)[/tex] is the vertex of the parabola.
Here, The equation of a parabola is,
[tex]- 8 (x - 5) = (y + 1)^2[/tex]
It can be written as,
[tex](x - 5) = \frac{(y + 1)^2}{-8}[/tex]
Add 5 on both sides,
[tex]x = \frac{(y + 1)^2}{-8} + 5[/tex]
Now, compare with the standard form of the equation of a parabola,
h = 5
k = - 1
Therefore, the vertex of the parabola is, (5, - 1).
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