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)

- anonymous

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- schrodinger

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- anonymous

@Australopithecus

- anonymous

campbell_st

- anonymous

@campbell_st

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## More answers

- anonymous

@Keigh2015

- anonymous

can you help??

- Keigh2015

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

- Keigh2015

@misssunshinexxoxo can you help this person with their math?

- anonymous

its okay

- anonymous

Hi

- misssunshinexxoxo

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

- campbell_st

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...

- anonymous

i got −(8x+1)(2x−3)

- campbell_st

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...?

- anonymous

one minute

- anonymous

-1\8 and 3\2

- anonymous

thats what i got

- campbell_st

ok so that's good
now part B is it a maximum or minimum...?

- campbell_st

you need to look at the sign of the leading coefficient

- anonymous

i have no clue @campbell_st

- triciaal

do you know what the coefficient is?

- campbell_st

what is the leading term in the equation..?

- anonymous

-16 ?

- campbell_st

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

- anonymous

oooh

- campbell_st

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

- anonymous

its both ??

- anonymous

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

- campbell_st

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

- campbell_st

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

- anonymous

max

- campbell_st

great...
now the vertex

- campbell_st

the easiest way is to find the line of symmetry
do you know about that...?

- anonymous

no

- triciaal

|dw:1437335587120:dw|

- anonymous

ookay

- campbell_st

ok the standard form of a quadratic is
\[0 = ax^2 + bx + c\]
the line of symmetry is found using
\[x = \frac{-b}{2 \times a}\]
in your question you have a = -16 and b = 22
you need to substitute the values into the equation to find x, the line of symmetry

- anonymous

1116

- anonymous

-11\16

- anonymous

@campbell_st

- campbell_st

nearly
x = 11/16 originally it was -22/-32
so you have the x value for the vertex, now substitute that value into the original equation to get the y value in the vertex...

- anonymous

umm

- anonymous

idk

- campbell_st

so its
\[f(11/16) = -16 \times (11/16)^2 + 22 \times (11/16) + 3\]
you need to calculate this value...

- anonymous

idk

- anonymous

i hate this question, its so hard

- anonymous

@campbell_st

- campbell_st

ok.... I have to go anyway.

- anonymous

okay

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