Question

How do you find the domain, range, intercepts and vertex of `f(x)=-x^2-2x+3`?

Answer 1

Factorise the quadratic equation

Explanation:

From
`y=-x^2-2x+3` ,
it can be factorised to
`y=(-x+1)(x+3)`

From this, you can see that it must intercept the x axis at -1 and 3 (solve the equation for `y=0`)

The x-coordinate of the turning point is halfway between the x intercepts, which you could either find mentally or use
`(-1+3)/2=1`
With your x-coordinate, you can substitute it into the original equation for the y-coordinate thus;
`y=-(1)^2-2(1)+3=4`
Therefore the vertex is `(1,4)`

Now that you know the vertex, and from the given function you know that it is a negative parabola, the range must be equal to or below the y-coordinate of the vertex (which is 4)

The domain is defined for all real values of x.