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The function $\bm{f}(\bm{x})=\frac{1}{9}(x-7)^{2}+3$ gives a metal ball's height above the ground $\bm{f}(\bm{x})$, in inches, $\bm{x}$ seconds after it started moving on a track, where $0\leq\bm{x}\leq 10$. Which of the following is the best interpretation of the vertex of the graph of $\bm{y}=\bm{f}(\bm{x})$ in the $xy$-plane?

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$5x^{2}+10x+16=0$

How many distinct real solutions does the given equation have?

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If $f(x)=\frac{x^{2}-6x+3}{x-1}$ what is $f(-1)$?

MathAdvanced Math

The expression $\frac{1}{3}x^{2}-2$ can be rewritten as $\frac{1}{3}(x-k)(x+k)$, where $k$ is a positive constant. What is the value of $k$?

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$f(x)=x^{3}+3x^{2}-6x-1$

For the function $f$ defined above, what is the value of $f(-1)$?

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$f(x)=x^{3}-9x$

$g(x)=x^{2}-2x-3$

Which of the following expressions is equivalent to $\frac{f(x)}{g(x)}$, for $x>3$?

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Which expression is a factor of $2x^{2}+38x+107$

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$(x-1)^{2}=-4$

How many distinct real solutions does the given equation have?

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$$y=0.25x^{2}-7.5x+90.25$$

The equation gives the estimated stock price $y$ in dollars, for a certain company $x$ days after a new product is launched, where $0\leq x\leq 20$. Which statement is the best interpretation of $(x,y)=(1,83)$ in this context?

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The expression $4x^{2}+bx-45$, where $b$ is a constant, can be rewritten as $(hx+k)(x+j)$, where $h$, $k$, and $j$ are integer constants. Which of the following must be an integer?

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$5x^{2}-37x-24=0$

What is the positive solution to the given equation?

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In the $xy$-plane, the $y$-coordinate of the $y$-intercept of the graph of the function $f$ is $c$. Which of the following must be equal to $c$ ?

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The expression $\frac{x^{-2}y^{\frac{1}{2}}}{x^{\frac{1}{3}}y^{-1}}$, where $x>1$ and $y>1$, is equivalent to which of the following? 

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$\bm{f(x)=5,470(0.64)}^{\frac{x}{2}}$

The function $\bm{f}$ gives the value, in dollars, of a certain piece of equipment after $\bm{x}$ months of use. If the value of the equipment decreases each year by $\bm{p}\%$ of its value the preceding year, what is the value of $\bm{p}$?

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The product of two positive integers is 546. If the first integer is 11 greater than twice the second integer, what is the smaller of the two integers?

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$$f(x)=(x+6)(x+5)(x-4)$$

The function $f$ is given. Which table of values represents $y=f(x)-3$?

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Which expression is equivalent to $(2x^{2}-4)-(-3x^{2}+2x-7)$?

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The population $P$ of a certain city $y$ years after the last census is modeled by the equation below, where $r$ is a constant and $P_{0}$ is the population when $y=0$.

$P=P_{0}(1+r)^{y}$

If during this time the population of the city decreases by a fixed percent each year, which of the following must be true?

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The expression $\frac{24}{6x+42}$ is equivalent to $\frac{4}{x+b}$, where $b$ is a constant and $x>0$. What is the value of $b$?

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$\sqrt{2x + 6} + 4 = x + 3$

What is the solution set of the equation above?

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From 2005 through 2014, the number of music CDs sold in the United States declined each year by approximately 15% of the number sold the preceding year. In 2005, approximately 600 million CDs were sold in the United States. Of the following, which best models $C$, the number of millions of CDs sold in the United States, $t$ years after 2005?

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$(x+2)(x+3)=(x-2)(x-3)+10$

Which of the following is a solution to the given equation?

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In the expression $3(2x^{2}+px+8)-16x(p+4)$, $p$ is a constant. This expression is equivalent to the expression $6x^{2}-155x+24$. What is the value of $p$?

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$x^{2}+6x + 4$

Which of the following is equivalent to the expression above?

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$$\frac{14x}{7y}=2\sqrt{w+19}$$

The given equation relates the distinct positive real numbers $w$, $x$, and $y$. Which equation correctly expresses $w$ in terms of $x$ and $y$?

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