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

May 8, 2017

#### Explanation:

From
$y = - {x}^{2} - 2 x + 3$ ,
it can be factorised to
$y = \left(- x + 1\right) \left(x + 3\right)$

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
$\frac{- 1 + 3}{2} = 1$
With your x-coordinate, you can substitute it into the original equation for the y-coordinate thus;
$y = - {\left(1\right)}^{2} - 2 \left(1\right) + 3 = 4$
Therefore the vertex is $\left(1 , 4\right)$

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.