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When the quadratic function $\bm{f}$ is graphed in the $xy$-plane, where $\bm{y}=\bm{f}(\bm{x})$, its vertex is $(-3,6)$. One of the $x$-intercepts of this graph is $\left(-\frac{17}{4},0\right)$. What is the other $x$-intercept of the graph?
Difficulty: Hard
A:
$(-\frac{29}{4},0)$
B:
$(-\frac{7}{4},0)$
C:
$(\frac{5}{4},0)$
D:
$(\frac{17}{4},0)$
The function $f$ is defined by $f(x)=(x+3)(x+1)$ . The graph of $f$ in the $xy$-plane is a parabola. Which of the following intervals contains the $x$-coordinate of the vertex of the graph of $f$ ?
Difficulty: Hard
A:
$-4<x<-3$
B:
$-3<x<1$
C:
$1<x<3$
D:
$3<x<4$
$x+y=12$
$y=x^{2}$
If $(x,y)$ is a solution to the system of equations above, which of the following is a possible value of $x$?
Difficulty: Easy
A:
0
B:
1
C:
2
D:
3
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