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$2x^{2}-2=2x+3$
Which of the following is a solution to the equation above?
Difficulty: Hard
A:
$2$
B:
$1 -\sqrt{11}$
C:
$\dfrac{1}{2}+\sqrt{11}$
D:
$\dfrac{1+\sqrt{11}}{2}$
$$f(x)=ax^{2}+4x+c$$
In the given quadratic function, \(a\) and \(c\) are constants. The graph of \(y=f(x)\) in the \(xy\)-plane is a parabola that opens upward and has a vertex at the point \((h,k)\), where \(h\) and \(k\) are constants. If \(k<0\) and \(f(-9)=f(3)\), which of the following must be true?
I. \(c<0\)
II. \(a\geq 1\)
Difficulty: Hard
A:
I only
B:
II only
C:
I and II
D:
Neither I nor II
$f(x)=4x^{2}+64x+262$
The function $g$ is defined by $g(x)=f(x+5)$. For what value of $x$ does $g(x)$ reach its minimum?
Difficulty: Hard
A:
$-13$
B:
$-8$
C:
$-5$
D:
$-3$
Which expression is equivalent to $11x^{3}-5x^{3}$?
Difficulty: Easy
A:
$16x^{3}$
B:
$6x^{3}$
C:
$6x^{6}$
D:
\(16x^{6}\)
Which expression is equivalent to $50x^{2}+5x^{2}$?
Difficulty: Easy
A:
$250x^{2}$
B:
$10x^{2}$
C:
$45x^{2}$
D:
$55x^{2}$
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