THETA DIVISION

Question 100

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Question

Questions #10-12 all concern the same quadratic. Given

f(x)=ax^2+bx+c

where

a,b,c\in\mathbb Z

, Dorin rewrites the function in vertex form, giving

f(x)=a(x-h)^2+11

. Which of the following must be true?

\begin{array}{ll} \text{I.} & f(x)\text{ must have two non-real, complex roots}\\ \text{II.} & f(x)\text{ must have a double root at }x=h\\ \text{III.} & f(x)\text{ must have an axis of symmetry at }x=11 \end{array}

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Question

Questions #10-12 all concern the same quadratic. Given

f(x)=ax^2+bx+c

where

a,b,c\in\mathbb Z

, Dorin rewrites the function in vertex form, giving

f(x)=a(x-h)^2+11

. Which of the following must be true?

\begin{array}{ll} \text{I.} & f(x)\text{ must have two non-real, complex roots}\\ \text{II.} & f(x)\text{ must have a double root at }x=h\\ \text{III.} & f(x)\text{ must have an axis of symmetry at }x=11 \end{array}