Question

How do you find the vertex and axis of symmetry for `y = 4x^2 + 7`?

Answer 1

The vertex is at `(x,y) = (0,7)`
The axis of symmetry is `x=0`

Explanation:

The general vertex form for a quadratic is
`color(white)("XXXX")` `y = m(x-a)^2+b`
`color(white)("XXXXXXXX")`where the vertex is at `(a,b)`

`y=4x^2+7` can easily be transformed into vertex form as:
`color(white)("XXXX")` `y = 4(x-0)^2+7`
`color(white)("XXXXXXXX")`where the vertex is at `(0,7)`

The equation is that of a parabola in standard position (opening upward), so the axis of symmetry is a vertical line through the vertex
i.e. `x=0`