Question

Given the graph of y=ax^2+bx+c where a,b,c are real numbers, if a=b=c the graph has no x-intercepts. True or False? Explain.

Answer 1

hint: use the discriminant formula D = b^2 - 4ac

Answer 2

If D < 0, then there are no x-intercepts

Answer 3

So there is no x-intercepts since they are all the same number?

Answer 4

@jim_thompson5910

Answer 5

a=b=c means we can replace every letter with say b


D = b^2 - 4ac
D = b^2 - 4bc ... replace 'a' with b
D = b^2 - 4b*b ... replace c with b
D = b^2 - 4b^2
D = -3b^2

Answer 6

b^2 is never negative
the -3 out front of b^2 makes -3b^2 always negative or 0

so if b = 0, then you'll have one x-intercept

otherwise, if b is nonzero, then D = -3b^2 is always negative making ax^2 + bx + c = 0 have no real solutions (so no x-intercepts)

Answer 7

gotcha! Thanks!