Practice Test 47 - Algebra 2

20 questions. Answer them in any order, then submit to see your score and every explanation.

A ball is thrown upward from a platform. Its height above the ground after $t$ seconds is modeled by $h(t)=-16t^2+48t+10$ , where $h$ is in feet. Graph the function for $0\le t\le 4$ with appropriate labels and a reasonable scale. Which choice shows the best axes labels and scale for this graph?
Complex numbers can be treated like points: $z=a+bi\leftrightarrow(a,b)$ . The distance between $z_1=a+bi$ and $z_2=c+di$ is the modulus $|z_1-z_2|=\sqrt{(a-c)^2+(b-d)^2}$ , and the midpoint is $\dfrac{z_1+z_2}{2}$ . For $z_1=-3+1i$ and $z_2=1-3i$ , what are the distance and the midpoint?
After restricting $f(x)=x^2$ to the domain $x\le 0$ so it becomes one-to-one, what is the inverse function $f^{-1}(x)$ ?
Convert the complex number $3+4i$ from rectangular form $a+bi$ to polar form $r(\cos\theta+i\sin\theta)$ . Use $r=\sqrt{a^2+b^2}$ and $\theta=\arctan\left(\frac{b}{a}\right)$ (with quadrant adjustment). The argument $\theta$ is measured counterclockwise from the positive real axis.
A bacteria culture grows according to $N(t)=3,200(1.25)^t$ , where $t$ is measured in hours and $N(t)$ is the number of bacteria. What is the growth rate as a percent per hour for this model?
Use structure to factor the expression $8x^3+27$ by recognizing it as a sum of cubes.
Addition of complex numbers can be interpreted as vector addition on the complex plane. If $z_1 = 1 + 4i$ and $z_2 = -3 + 2i$ , what point corresponds to $z_1 + z_2$ ?
Let $f(x)=5(x-2)^2+7(x-2)-3.$ If you chunk the repeated sub-expression by letting $u=(x-2)$ , which rewritten form best reveals the structure without fully expanding?
Two polynomials and one exponential are given: $f(x)=x^2$ (quadratic), $g(x)=x^5$ (5th degree), and $h(x)=1.1^x$ (exponential). Which statement about eventual behavior is true?
Prove the identity $(a-b)^3 = a^3 - 3a^2 b + 3 a b^2 - b^3$ by expanding $(a-b)^3$ , then apply it to expand $(x-2)^3$ .
If $\log_{10}(x)=2$ , find $x$ by rewriting in exponential form.
A scientist records a sample's mass (in grams) after each processing step: Step $n$ : 0, 1, 2, 3 Mass $M(n)$ : 200, 180, 162, 145.8 Classify the pattern and identify the constant percent rate per step.
List all terms and their coefficients in the expression $-x^2 + \frac{2}{3}x - 5$ . (Remember $-x^2$ has an implicit coefficient of $-1$ .)
Solve the quadratic equation by completing the square: $x^2 + 8x + 7 = 0.$ Write your work in the form $(x - p)^2 = q$ before solving.
Which matrix equation $AX=B$ correctly matches the system (use variable order $x, y$ )? $\begin{cases} 4x-y=2\\ -3x+6y=15 \end{cases}$ (You can verify by noting that multiplying $A$ by $X$ produces the left-hand sides of the two equations.)
Consider the expression $-3x^2 + 12x + 36$ . After factoring completely to reveal the zeros, how many distinct real zeros does the function $h(x) = -3x^2 + 12x + 36$ have?
Points $z_1=4-i$ and $z_2=2+5i$ are plotted on the complex plane (so $a+bi$ corresponds to $(a,b)$ ). Using the midpoint formula $\dfrac{z_1+z_2}{2}=\dfrac{a+c}{2}+\dfrac{b+d}{2}i$ , what is the midpoint of the segment joining $z_1$ and $z_2$ ?
The table shown displays the relationship between the side length $s$ of a square and its area $A$ . Based on this data, which equation correctly models the relationship, and what would be the most appropriate viewing window for graphing this function?
On the complex plane, the point $z=a+bi$ corresponds to the coordinate $(a,b)$ . The distance between $z_1=a+bi$ and $z_2=c+di$ is $|z_1-z_2|=\sqrt{(a-c)^2+(b-d)^2}$ , and the midpoint is $\dfrac{z_1+z_2}{2}=\dfrac{a+c}{2}+\dfrac{b+d}{2}i$ (the same as the coordinate geometry formulas). For $z_1=1-3i$ and $z_2=5+i$ , what are the distance between them and the midpoint of the segment joining them?
On the coordinate plane, the graph of $f(x)=|x|$ is shown along with the graph of $g(x)$ (a V-shape) whose vertex is at $(2,0)$ and which has the same shape as $f(x)$ . Which function could be $g(x)$ ?

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