3
advanced-math

The graph of y=ax2+bx+cy = ax^2 + bx + c passes through the origin. What must be true?

A

c=0c = 0

B

b=0b = 0

C

a=0a = 0

D

c=1c = 1

Correct Answer: A

Choice A is the correct answer. Passing through the origin means the point (0,0)(0, 0) is on the graph.

  1. Substitute x=0x=0 and y=0y=0 into the equation.
  2. 0=a(0)2+b(0)+c0 = a(0)^2 + b(0) + c.
  3. 0=0+0+c⇒c=00 = 0 + 0 + c \Rightarrow c = 0.

Choice B is incorrect because bb affects the vertex position. Choice C is incorrect because then it wouldn't be quadratic. Choice D is incorrect because then y-intercept would be 1.

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Set 9: Quadratic Equations and Functions 9