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

1 Answer
May 8, 2017

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.