I am to find the equation of the axis of symmetry and the coordinate of the vertex of the graph of each function. I don't undertand

y=2x^2+4

y= 2(x+0)^2 +4

the axis of symettry is x=0, or the y axis. vertex: (0,4)

To find the equation of the axis of symmetry and the coordinates of the vertex of the graph of a quadratic function, you can use a few steps:

Step 1: Identify the coefficients of your quadratic function. In your case, the quadratic function is y = 2x^2 + 4. The coefficient of x^2 is 2, and the constant term is 4.

Step 2: The equation for the axis of symmetry is given by x = -b/2a, where a is the coefficient of x^2 and b is the coefficient of x. In your case, a = 2 and b = 0 (since the coefficient of x is 0 in your function), so the equation for the axis of symmetry is x = -0/(2*2) = 0.

Step 3: To find the vertex, substitute the x-value from the equation of the axis of symmetry into the original function and solve for y. In your case, substitute x = 0 into y = 2x^2 + 4:
y = 2(0)^2 + 4
y = 0 + 4
y = 4

So, the coordinates of the vertex are (0, 4).

In summary:
- The equation of the axis of symmetry is x = 0.
- The coordinates of the vertex are (0, 4).