y=x^2 +4x-12, Find the Range (co-domain) when the domain of x is (1) -6 to 2 inclusive (2) the set of real numbers, R.
This question usually comes up at AS level where students have prior knowledge of quadratic functions:We need to 1) understand the 'shape' 2) locate the roots 3) Find the turning point 4) sketch the graph 5) answer1) Quadratic graphs have the x^2 functional form. This produces a 'smiley face'. (Draw)2) Some quadratic graphs intersect the x-axis, some don't. (Draw) The points where the smiley face intersects the axis are the roots. We can have 2, 1, or none.3) The turning point is the lowest tip of the smiley face.4) The 'domain' is all the values x can take, the 'range' is all the values y can takeTurning to our example:1&2) Roots: x = -6, 2 3)Turning point: (-2, -16) 4)(now sketch)5) when x in [-6,2] y in [-16,0] when x in R, y in [-16,inf)
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