8, -14). Write the equation of the parabola in vertex form.(1 point) Responses y=3(x−6)2−6 y is equal to 3 times open paren x minus 6 close paren squared minus 6 y=−2(x−6)2−6 y is equal to negative 2 times open paren x minus 6 close paren squared minus 6 y=(x+6)2−6 y is equal to open paren x plus 6 close paren squared minus 6 y=−3(x+6)2−6 what is the correct answer
The correct answer is y=(x+6)2−6.
To write the equation of the parabola in vertex form, we need to use the vertex coordinates. In this case, the vertex is (8, -14).
The vertex form of a parabola equation is given by:
y = a(x - h)^2 + k
where (h, k) represents the coordinates of the vertex.
Therefore, substituting the given vertex coordinates (8, -14), we get:
y = a(x - 8)^2 - 14
So, out of the provided options, the correct answer is: y = a(x - 8)^2 - 14.
To write the equation of a parabola in vertex form, we need to know the coordinates of the vertex. In this case, the given coordinates of the vertex are (8, -14).
The vertex form of a parabola equation is given by:
y = a(x - h)^2 + k
Where (h, k) represents the vertex coordinates. Plugging in the given vertex coordinates (8, -14), we get:
y = a(x - 8)^2 - 14
Now, to determine the value of 'a' (the coefficient in front of the squared term), we need additional information. If we have any other point on the parabola, we can substitute its coordinates (x, y) into the equation and solve for 'a'. However, with only the vertex given, there are multiple possibilities for the equation.
Unfortunately, without more information about the parabola, we cannot determine the single correct equation. Each of the given equations may be valid based on different situations or constraints.