Suppose a parabola has a vertex (6, -6) and also passes through the point (8, -14).
Write the equation of the parabola in vertex form.(1 point)
Responses
y=−2(x−6)2−6
�
=
−
2
(
�
−
6
)
2
−
6
y is equal to negative 2 times open paren x minus 6 close paren squared minus 6
y=−3(x+6)2−6
�
=
−
3
(
�
+
6
)
2
−
6
y is equal to negative 3 times open paren x plus 6 close paren squared minus 6
y=(x+6)2−6
�
=
(
�
+
6
)
2
−
6
y is equal to open paren x plus 6 close paren squared minus 6
y=3(x−6)2−6
�
=
3
(
�
−
6
)
2
−
6
y is equal to 3 times open paren x minus 6 close paren squared minus 6
None of the given responses is correct. The correct equation of the parabola in vertex form is:
y = (x - 6)^2 - 6
The equation of the parabola in vertex form is:
y = -2(x-6)^2 - 6.
To write the equation of a parabola in vertex form, you need to know the coordinates of the vertex and one other point on the parabola. In this case, the vertex is given as (6, -6) and the point (8, -14) is also on the parabola.
The vertex form of a parabola is y = a(x - h)^2 + k, where (h, k) is the vertex.
To find the value of "a", you can substitute the x and y coordinates of the point (8, -14) into the equation and solve for "a":
-14 = a(8 - 6)^2 - 6
-14 = a(2)^2 - 6
-14 = 4a - 6
-14 + 6 = 4a
-8 = 4a
a = -2
Now that we have the value of "a", we can substitute it along with the vertex coordinates into the vertex form equation:
y = -2(x - 6)^2 - 6
Therefore, the equation of the parabola in vertex form is y = -2(x - 6)^2 - 6.