Question

How do you find the vertex and intercepts for `4y=x^2+4`?

Answer 1

So `P_("vertex") -> (x,y) -> (0,+1)`
The only intercept is on the y-axis and that is at the vertex.

Explanation:

Standard quadratic form:`color(white)(...)y= ax^2+bx+c`

Given: `4y=x^2+4`

Write as: `y=1/4x^2 +1`

Let any point on the graph be P

There is no `bx` term so the graph is symmetrical about the y-axis

Consequently `x=0`

The whole plot is transformed upwards from y=0 by the +1 and the amount of upward transformation is +1

So `P_("vertex") -> (x,y) -> (0,+1)`