A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
An expression is shown below:
f(x) = 16x2 + 22x + 3
Part A: What are the xintercepts of the graph of the f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)
anonymous
 one year ago
An expression is shown below: f(x) = 16x2 + 22x + 3 Part A: What are the xintercepts of the graph of the f(x)? Show your work. (2 points) Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points) Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)

This Question is Closed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@UsukiDoll this is the last one im having trouble with, can you help me? please

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0part A: we have to solve the subsequent quadratic equation: \[\Large  16{x^2} + 22x + 3 = 0\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0can you help me with that? again im new to this...

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0I rewrite that equation as below: \[\Large 16{x^2}  22x  3 = 0\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0Next I compare that equation with this more general equation: \[\Large a{x^2} + bx + c = 0\] so we can write: a=16, b=22, and c=3 am I right?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0now, in order to find the requested xintercepts, you have to apply this formula: \[\Large x = \frac{{  b \pm \sqrt {{b^2}  4 \times a \times c} }}{{2 \times a}}\] what do you get?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0you have to substitute the values of a, b, and c into that formula: \[\Large \begin{gathered} x = \frac{{  b \pm \sqrt {{b^2}  4 \times a \times c} }}{{2 \times a}} = \hfill \\ \hfill \\ = \frac{{  \left( {  22} \right) \pm \sqrt {{{\left( {  22} \right)}^2}  4 \times 16 \times \left( {  3} \right)} }}{{2 \times 16}} = ...? \hfill \\ \end{gathered} \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i dont have a calculator at the moment, its hard doing it in my head

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0please use windows calculator

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0\[\Large \begin{gathered} x = \frac{{  b \pm \sqrt {{b^2}  4 \times a \times c} }}{{2 \times a}} = \hfill \\ \hfill \\ = \frac{{  \left( {  22} \right) \pm \sqrt {{{\left( {  22} \right)}^2}  4 \times 16 \times \left( {  3} \right)} }}{{2 \times 16}} = \hfill \\ \hfill \\ = \frac{{22 \pm \sqrt {484 + 192} }}{{32}} = ...? \hfill \\ \end{gathered} \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0mine isnt working at the moment...

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0next step: \[\Large \begin{gathered} x = \frac{{  b \pm \sqrt {{b^2}  4 \times a \times c} }}{{2 \times a}} = \hfill \\ \hfill \\ = \frac{{  \left( {  22} \right) \pm \sqrt {{{\left( {  22} \right)}^2}  4 \times 16 \times \left( {  3} \right)} }}{{2 \times 16}} = \hfill \\ \hfill \\ = \frac{{22 \pm \sqrt {484 + 192} }}{{32}} = \hfill \\ \hfill \\ = \frac{{22 \pm 26}}{{32}} = \begin{array}{*{20}{c}} {\frac{{22 + 26}}{{32}} = ...?} \\ {\frac{{22  26}}{{32}} = ...?} \end{array} \hfill \\ \end{gathered} \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0leaves you with 12/32

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0yes! and we can simplify them as below: \[\Large {x_1} = \frac{{48}}{{32}} = \frac{3}{2},\quad {x_2} =  \frac{4}{{32}} =  \frac{1}{8}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0your right, i was overr thinking..

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0so we got your xintercepts

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0Now, part B: the vertex of a parabola is the point at the top or the point at the bottom of a parabola

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0we have these subsequent cases: dw:1439456183056:dw

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0now, in our original equation: \[\Large f\left( x \right) =  16{x^2} + 22x + 3\] is a= 16, so what is your parabola?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0the coefficient of the second degree monomial od f(x) is 16, right?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0in that case, being 16 < 0, your parabola is concave down, namely your parabola is the one at the left place in my drawing dw:1439456653946:dw

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0now, the coordinate of the vertex, are given by the subsequent formulas: \[\Large {x_V} =  \frac{B}{{2A}},\quad {y_V} =  \frac{{{B^2}  4AC}}{{4A}}\] where A= 16, B=22, and C=3

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0what do you get?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0hint: \[\Large {x_V} =  \frac{B}{{2A}} =  \frac{{22}}{{2 \times \left( {  16} \right)}} = ...?\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0I got this: \[\Large {x_V} = \frac{{22}}{{32}} = \frac{{11}}{{16}}\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0now, we have to compute the ycoordinate, so we have: \[\Large \begin{gathered} {y_V} =  \frac{{{B^2}  4AC}}{{4A}} =  \frac{{{{22}^2}  4 \times \left( {  16} \right) \times 3}}{{4 \times \left( {  16} \right)}} = \hfill \\ \hfill \\ =  \frac{{484 + 192}}{{  64}} = ...? \hfill \\ \end{gathered} \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0my computer is acting up and this is all confusing to me, its my last question and im stressing

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0more precisely, we get this: \[\Large {y_V} = \frac{{676}}{{64}} = \frac{{169}}{{16}}\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0so the vertex V, of your parabola is the subsequent point: \[\Large V = \left( {\frac{{11}}{{16}},\frac{{169}}{{16}}} \right)\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0please wait, we have to solve part C

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes, im understanding everything, just upset that my computer isnt letting me use my cal.

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0in order to draw your parabola, it is suffice to draw the xintercepts and the vertex V into a xyplane, like this: dw:1439457756334:dw

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0then you have to draw a curve like this: dw:1439457886482:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0trying to put everything together in sentences for part c... sadly i cant send in my drawling

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0we can write this: step #1 I draw the xintercepts, and the vertex of my parabola, step#2 I connect those three points each other using a continuous line.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.