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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
$f(\theta)=-0.28(\theta-27)^{2}+880$
An engineer wanted to identify the best angle for a cooling fan in an engine in order to get the greatest airflow. The engineer discovered that the function above models the airflow $\bm{f}(\bm{\theta})$, in cubic feet per minute, as a function of the angle of the fan $\bm{\theta}$, in degrees. According to the model, what angle, in degrees, gives the greatest airflow?
Difficulty: Medium
A:
$-0.28$
B:
$0.28$
C:
$27$
D:
$880$
$$p=20+\frac{16}{n}$$
The given equation relates the numbers $p$ and $n$, where $n$ is not equal to $0$ and $p>20$. Which equation correctly expresses $n$ in terms of $p$?
Difficulty: Medium
A:
$n=\frac{p-20}{16}$
B:
$n=\frac{p}{16}+20$
C:
\(n=\frac{p}{16}-20\)
D:
$n=\frac{16}{p-20}$
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