Practice Test 8 - Algebra 1

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

Transform $x^2 - 4x + 1 = 0$ into the form $(x - p)^2 = q$ (an equivalent equation with the same solutions), then solve by taking square roots.
A student earns $15 each time they mow a lawn and already has $20 saved. Let $n$ be the number of lawns mowed and let $M$ be the total money saved (in dollars). What is an appropriate scale for graphing this relationship if $n$ is between 0 and 10 lawns?
Rewrite $y=2x^2-12x+1$ in vertex form $y=a(x-h)^2+k$ by completing the square.
Solve the inequality: $-2x+8 \le 4$
Solve by factoring: $x^2+7x+12=0$
If $g(x)=x^2-5x+6$ , what is the value of $g(3)$ ?
Simplify and rewrite $\frac{x^2-4}{x-2}$ in the form $q(x)+\frac{r(x)}{x-2}$ , with $\deg(r)<1$ .
A student is solving $\frac{2}{x}=6$ and writes: 1) $\frac{2}{x}=6$ 2) $2=6$ 3) $x=1$ Identify the error in the student work.
A farmer wants to describe egg production on their small farm over the last 30 days. Define 3–5 appropriate quantities (variables) with units that capture what is happening day to day.
What is the coefficient of $y$ in the expression $2y^2-y+6$ ?
Complete the square to find the vertex of $f(x)=x^2-8x+3$ . Give your answer as an ordered pair $(h,k)$ .
If $f(x)=x^2$ and $g(x)=2x-1$ , what is $f(g(x))$ ?
A line is given by $y=-2x+5$ . On a coordinate plane, what is the slope of this line?
What is the explicit formula for the arithmetic sequence with $a_1=3$ and common difference $d=4$ ?
A streaming service charges a $5 sign-up fee and then $8 per month. If $m$ is the number of months and $C$ is the total cost (in dollars), what should the axes be labeled when graphing this relationship on a coordinate plane?
To graph $y=x^2+7x+12$ , first factor to find where the parabola crosses the $x$ -axis. Where does the graph cross the $x$ -axis?
Given $P(x)=(x-1)^3(x+3)$ , what happens at the zero $x=1$ on the graph of $y=P(x)$ ?
A savings account balance is modeled by $A(t)=1000(1.05)^t$ , where $t$ is the number of years. What is the annual percent growth rate?
A bacteria culture is modeled by $P(t)=800(1.03)^t$ , where $t$ is measured in hours. Is this exponential growth, decay, or neither?
A researcher compares three growth models: $f(x) = 20x + 100$ (linear), $g(x) = 2x^3 - x^2 + 50$ (cubic polynomial), and $h(x) = 15(1.25)^x$ (exponential). At $x = 8$ , the values are approximately $f(8) = 260$ , $g(8) = 970$ , and $h(8) = 89$ . Based on the long-term growth characteristics of these function types, which function will eventually dominate for very large values of $x$ ?

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