Question

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

Answer 1

`"see explanation"`

Explanation:

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

`rArr-x^2+4=0rArrx^2=4rArrx=+-2`

`"the axis of symmetry is at the midpoint of the x-intercepts"`

`rArr"axis of symmetry is "x =(-2+2)/2=0`

`"that is the y-axis is the axis of symmetry"`

`"since coefficient of "x^2"term "<0`

`"then parabola has a maximum value "nnn`

`"to find the vertex let "x=0`

`rArry=0+4=4rArr(0,4)larrcolor(magenta)" vertex"`
graph{-x^2+4 [-10, 10, -5, 5]}