Find the largest value of c such that -2 is in the range of f(x)=x^2+3x+c.

WhichWitchIsWhich
Oct 29, 2017

#1**+2 **

x^2 + 3x + c

To have -2 remain in the range...since this parabola turns upward..it must be that the vertex is at (a, -2)

The x coordinate of the vertex is given by -3/ [2 * 1] = -3/2

So.....it must be that

(-3/2)^2 + 3(-3/2) + c = -2 simplify

9/4 - 9/2 + c = -2

-9/4 + c = -2

-9/4 + c = -8/4 add 9/4 to both sides

1/4 = c ⇒ any larger value takes -2 out of the range

See the graph here : https://www.desmos.com/calculator/b25akxl65z

CPhill
Oct 29, 2017