Question

An expression is shown below:

f(x) = –16x2 + 22x + 3

Part A: What are the x-intercepts 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)

Answer 1

@Australopithecus

Answer 2

campbell_st

Answer 3

@campbell_st

Answer 4

@Keigh2015

Answer 5

can you help??

Answer 6

I am sorry this type of math is not my strong suit.

Answer 7

@misssunshinexxoxo can you help this person with their math?

Answer 8

its okay

Answer 9

Hi

Answer 10

This might help http://www.wolframalpha.com/input/?i=f%28x%29+%3D+%E2%80%9316x2+%2B+22x+%2B+3

Answer 11

well you need to factor the equation

start with factoring out the negative...

\[f(x) = -(16x^2 - 22x - 3)\]

next multiply 16 and - 3 so -48

find the factors of -48 that add to -22 the larger factor is negative
its a relatively easy pair to find...

Answer 12

i got −(8x+1)(2x−3)

Answer 13

that's correct so so to find the x-intercepts you need to solve

8x + 1 = 0 and 2x - 3 = 0

what values do you get...?

Answer 14

one minute

Answer 15

-1\8 and 3\2

Answer 16

thats what i got

Answer 17

ok so that's good

now part B is it a maximum or minimum...?

Answer 18

you need to look at the sign of the leading coefficient

Answer 19

i have no clue @campbell_st

Answer 20

do you know what the coefficient is?

Answer 21

what is the leading term in the equation..?

Answer 22

-16 ?

Answer 23

so if its positive then you have a minimum, if its negative you have a maximum

Answer 24

oooh

Answer 25

great so which do you have, max or min...?

Answer 26

its both ??

Answer 27

-1\8 is max and and 3\2 in min >??

Answer 28

no if the leading coefficient is negative... do you have a max or min,,, it can't be both

Answer 29

here is the equation

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

you said the leading coefficient is -16

that's correct...

so if its a potive value you have a minimum if its negative you have a maximum

so which do you choose

Answer 30

max

Answer 31

great...

now the vertex

Answer 32

the easiest way is to find the line of symmetry

do you know about that...?

Answer 33

no