Given f(x) = 11x^2 + 13x - 28, use the discriminant to determine whether or not f(x) ever equals -100 for any values of x.

ihavelovedyousincewewere18
Jan 29, 2015

#1**+5 **

The discriminant = b^2 - 4ac.... so we have

13^2 - 4(11)(-28) = > 0 so this tells us we have real roots

But...maybe I'm missing something.....the discriminant doesn't tell us anything about whether or not f(x) ever = -100....it just tells us whether or not we may have "real" zeroes

We'd need to find the vertex for this

The x coordinate for the vertex is given by -b/2a = -13/2(11) = -13/22

And putting this back into the function.....we have the y value at the vertex = about -31.84

And since this parabola turns "up," (-13/22, -31.84) is the lowest point on the graph.....so f(x) never = -100....

CPhill
Jan 29, 2015

#2**+10 **

Best Answer

If you added 100 to f(x) then you would know.

$$\\11x^2+13x-28+100=0\\

11x^2+13x+72=0\\

\triangle=b^2-4ac\\

\triangle=13^2-4*11*72\\

\triangle<0\\

$therefore the graph will never reach as low as $ f(x)=-100$$

Melody
Jan 29, 2015