Answered

At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Explore our Q&A platform to find reliable answers from a wide range of experts in different fields. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

PLEASE HELP
Use the function f(x) to answer the questions.

f(x) = −16x2 + 22x + 3

Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)

Part B: Is the vertex of the graph of f(x) going to be a maximum or a 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)

Sagot :

First graph

  • y=-16x^2+22x+3(Graph attached)

#A

Use quadratic formula

[tex]\\ \rm\rightarrowtail x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]\\ \rm\rightarrowtail x=\dfrac{-22\pm\sqrt{484+192}}{-32}[/tex]

[tex]\\ \rm\rightarrowtail x=\dfrac{-22\pm\sqrt{676}}{-32}]/tex]

[tex]\\ \rm\rightarrowtail x=\dfrac{-22\pm 26}{-32}[/tex]

[tex]\\ \rm\rightarrowtail x=\dfrac{-1}{8}\:or\:\dfrac{3}{2}[/tex]

[tex]\\ \rm\rightarrowtail x=-0.125\:or\:1.5[/tex]

#B

Vertex will be maximum

Coordinates are

  • (0.688,10.563)

#C

  • We have to find x intercepts (Part A)
  • Then vertex(Part B)
  • Then we can graph it

View image Аноним
fieryanswererft

[tex]\sf f(x) = -16x^2 + 22x + 3[/tex]

Part A

To find x-intercepts, the f(x) will be 0

[tex]\sf \hookrightarrow -16x^2 + 22x + 3=0[/tex]

[tex]\sf \hookrightarrow -16x^2 + 24x -2x+ 3=0[/tex]

[tex]\sf \hookrightarrow -8x(2x-3)-1(2x- 3)=0[/tex]

[tex]\sf \hookrightarrow (-8x-1)(2x+ 3)=0[/tex]

[tex]\sf \hookrightarrow -8x-1=0 , \ 2x+ 3=0[/tex]

[tex]\sf \hookrightarrow x=-0.125 , \ x=1.5[/tex]

find y-intercept:

to find y-intercept, x will be 0

[tex]\sf f(x) = -16(0)^2 + 22(0) + 3[/tex]

[tex]\sf f(x) = 3[/tex]

Part B

To find vertex use the formula: x = -b/2(a)

[tex]\sf \rightarrow x = \dfrac{-22}{2(-16)}[/tex]

[tex]\sf \rightarrow x = 0.6875[/tex]

find y coordinates:

[tex]\sf f(x) = -16(0.6875)^2 + 22(0.6875) + 3[/tex]

[tex]\sf f(x) =10.5625[/tex]

coordinates of vertex: (0.6875, 10.5625)

  • [tex]\bold{\mathrm{If}\:a < 0,\:\mathrm{then\:the\:vertex\:is\:a\:maximum\:value}}[/tex]
  • [tex]\bold{\mathrm{If}\:a > 0,\:\mathrm{then\:the\:vertex\:is\:a\:minimum\:value}}[/tex]  

As its positive and greater than 0, the vertex will be Maximum.

part C

To draw the graph, simplify point the vertex on the graph. Then point both the x-intercepts. Also the y-intercept and draw the curve with free hand.

Graph attached:

View image fieryanswererft
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.