If in applying the quadratic formula to a quadratic equation f(x) = ax^2 + bx + c = 0 it happens that c=b^2/4a , then the graph of y = f(x) will certainly:
(A) have a maximum
(B) have a minimum
(C) have a tangent parallel to the x-axis
(D) have a tangent parallel to the y-axis
Answers
Given : f(x) = ax^2 + bx + c = 0 it happens that c=b^2/4a
To find : graph of y = f(x) will have certainly
Step-by-step explanation:
y = f(x) = ax² + bx + c
=>dy/dx = f'(x) = 2ax + b
putting dy/dx = 0
=> 2ax + b = 0
=> x = - b/2a
d²y/dx² = f''(x) = 2a
=> f(x) can have minimum or maximum value at x = -b/2a depending upon sign of a ( + ve or - ve)
dy/dx = f'(x) = 2ax + b
putting x = - b/2a ( where maxima or minima exist)
we get slope of tangent
= 2a(-b/2a) + b
= -b + b
= 0
Slope of tangent = 0
=> Hence tangent is certainly Parallel to x - axis .
option C is correct
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Answer:
Please refer to the attachment.
