Question

How do you find the vertex and the intercepts for `f(x) =x^2 + 3`?

Answer 1

`"see explanation"`

Explanation:

`"for a quadratic in the form "y=x^2+c`

`"the vertex has coordinates "=(0,c)`

`"here "c=3`

`color(magenta)"vertex "=(0,3)`

`"to find the x-intercepts let y = 0"`

`x^2+3=0rArrx^2=-3`

`"this has no real solutions, hence no x-intercepts"`
graph{x^2+3 [-10, 10, -5, 5]}