Question

Help me please!!!

Answer 1

16. What is the equation, in standard form, of a parabola that models the values in the table?
x –1 0 2
f(x) 10 5 13
(1 point)
y = 3x2– 2x + 5
y = x2– 2x + 5
y = 2x2– 3x + 5
y = –3x2+ 2x + 5

Answer 2

12. Last night, Julie’s pet hamster Zoe kept Julie awake for at least an hour running on her exercise wheel and scratching at the corner of her cage. Zoe ran on the wheel at least twice as long as she scratched at the corners of her cage, and she spent more than hour running on her wheel. Which system of inequalities represents the time Zoe kept Julie awake last night if x is the number of hours Zoe spent running on her wheel and y is the number of hours spent scratching her cage? (1 point)

Answer 3

For 16: You can plug in the values of \(x=-1,0,2\) into each choice and see which one gives you the f(x) values in the table. Alternatively, we can approach the problem in the following manner. Recall that a quadratic function in standard form is given by the function \(f(x) = ax^2+bx+c\). In the table, we're told that \(f(-1)=10\), \(f(0) = 5\) and \(f(2) =13\). If we make these substitutions into our quadratic function, we generate the following system of equations in terms of the unknown coefficients \(a,\,b,\) and \(c\): $$\left\{\begin{aligned}a-b+c&= 10\\ c &= 5\\4a +2b + c &= 13\end{aligned}\right.$$Since we see right away that \(c=5\), then it follows that we can reduce the system of equations as follows:$$\left\{\begin{aligned}a-b+c&= 10\\ c &= 5\\4a +2b + c &= 13\end{aligned}\right. \implies \left\{\begin{aligned}a-b &= 5\\ 4a+2b&= 8\end{aligned}\right.\implies \left\{\begin{aligned}a-b &= 5\\ 2a+b &= 4\end{aligned}\right.$$Can you take things from here and solve for \(a\) and \(b\)? :-)

For 12: There seems to be something missing from the problem statement. Is this sentence supposed to read "Zoe ran on the wheel at least twice as long as she scratched at the corners of her cage, and she spent more than *1/4* hour running on her wheel."? If so, then if Zoe ran (x) AT LEAST twice as long as she scratched (y), then that means that x __ 2y (fill in the blank). Likewise if she ran and scratched for MORE THAN one hour, that means that x+y __ 1 (fill in the blank). Last, but not least, Zoe ran MORE THAN 1/4 hour (assuming that I filled in the missing info properly), so that means that x __ 1/4 (fill in the blank). if you pay attention to the words I put in caps, the type of inequality symbol that needs to be used should become more apparent. If you have questions about what I wrote here, don't hesitate to ask! :-)

I hope this made sense! :-)

Answer 4

Not quite. :-/

For 16, I get a=3 and b=-2 (with c=5 already being obvious), which leads to the answer A. I would recommend checking over your work.

I overlooked something for 12. When it says that "Julie’s pet hamster Zoe kept Julie awake for AT LEAST an hour running on her exercise wheel and scratching at the corner of her cage" implies that \(x+y\geq 1\). The part where it says that she ran more than 1/4 hours, that means that \(x>1/4\), and the part that says she ran AT LEAST twice as long as she ran means that \(x\geq 2y\). So putting everything together gives us \(x+y\geq 1\), \(x>1/4\) and \(x\geq 2y\), which is choice C.

I hope this clarifies things! :-)