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

1 Answer
Tilly
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.

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