Which statement must be true if a parabola represented by the equation y = ax2 + bx + c does not...?

Question

Which statement must be true if a parabola represented by the equation y = ax2 + bx + c does not intersect the x-axis?


A) b2 - 4ac = 0
B) b2 - 4ac < 0
C) b2 - 4ac > 0, and b2 - 4ac is a perfect square.
D) b2 - 4ac > 0, and b2 - 4ac is not a perfect square.




and why?

Answer 1

B

Answer 2

B would be the correct answer. The reason for this goes back to the quadratic equation: x=(-b+/-Sqrt(b^2-4ac))/2a.

This requires that you take the square root of b^2-4ac to get the roots of the parabola. If it is negative then you cannot take the square root. That means the parabola has no real roots. As far as a picture goes, having no real roots implies that there is no intersection with the x-axis.

Answer 3

replace (-2, -3), (a million,5), and (4, -2) into y = ax2 + bx + c -3=4a-2b+c (a million) 5=a+b+c (2) -2=16a+4b+c (3) (3)-(2) -7 = 15a+3b (4) (a million)-(2) -8 = 3a-3b (5) (4)+(5) -15=18a a = -5/6 replace a into (5) -8=3(-5/6)-3b -8=-5/2-3b 8= 5/2+3b 3b=8-5/2 3b=16/2-5/2 3b=11/2 b=11/6 replace a and b into (2) 5=a+b+c 5=-5/6+11/6+c 5=6/6+c 5=a million+c c=4 a=-5/6 b=11/6 c=4 y=-5/6x2+11/6x+4

Answer 4

B) because x =((-b+-sqrt(b^2-4c))/2a and negative numbers don´t have sqrts