SOLUTION: If h (x) = a x 2 + bx + c, where b 2 - 4ac < 0 and a < 0, which of the following statements must be true?
I. The graph of h (x) has no points in the first
or second quadrants.
I
Algebra ->
Quadratic Equations and Parabolas
-> SOLUTION: If h (x) = a x 2 + bx + c, where b 2 - 4ac < 0 and a < 0, which of the following statements must be true?
I. The graph of h (x) has no points in the first
or second quadrants.
I
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Question 329600: If h (x) = a x 2 + bx + c, where b 2 - 4ac < 0 and a < 0, which of the following statements must be true?
I. The graph of h (x) has no points in the first
or second quadrants.
II. The graph of h (x) has no points in the third
or fourth quadrants.
III. The graph of h (x) has points in all quadrants.
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) None of the statements are true. Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! if b^2 - 4ac is smaller than 0, then the roots are not real which means that the equation does not cross the x-axis.
If a is less than 0, this means that the graph of the equation points up and opens down.
Take these two together and the graph of the equation must be below the x-axis.
Statement 1 looks true.
Statement 2 looks false.
Statement 3 looks false.
I would say the answer is statement 1 only, which would be selection A.
A graph that meets the criteria expressed above would be:
-x^2 + x - 1
In this equation:
a = -1
b = 1
c = -1
b^2 - 4ac would be equal to 1 - (4*-1*-1) = 1 - (4) = -3 which is < 0.
a = -1 which is < 0.
The graph of this equation looks like this:
You can see that the graph of this equation is in Quadrants III and IV only.
