we know that
If the vertex is on the y-axis, then the x-coordinate of the vertex is equal to zero
we are going to verify the vertex of each one of the functions to determine the solution
Remember that
The equation in vertex form of a vertical parabola is equal to
where
(h,k) is the vertex
if -------> the parabola open upward (vertex is a minimum)
if -------> the parabola open downward (vertex is a maximun)
<u>case A)</u>
This is a vertical parabola open upward
the vertex is the point
therefore
The function does not have a vertex on the y-axis
<u>case B)</u>
convert to vertex form
Complete the square. Remember to balance the equation by adding the same constants to each side.
Rewrite as perfect squares
the vertex is the point
therefore
The function does not have a vertex on the y-axis
<u>case C)</u>
the vertex is the point
The x-coordinate of the vertex is equal to zero
therefore
The function has a vertex on the y-axis
<u>case D)</u>
convert to vertex form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
Complete the square. Remember to balance the equation by adding the same constants to each side.
Rewrite as perfect squares
the vertex is the point
therefore
The function does not have a vertex on the y-axis
<u>the answer is</u>