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.

Answer 1

this is 16 and 22 right?

Answer 2

not quite?
x intercepts is when y = 0
or in this case f(x) = 0
so 0 = -16x^2 + 22x + 3 solve for x

Answer 3

I honestly have no idea how to do that...do i combine liker terms?

Answer 4

there are not like terms because each has a different number of x's ... if that makes any sense?...
you would use the quadratic equation http://2.bp.blogspot.com/_9xX2yNGJA4E/TPm214sFVjI/AAAAAAAAADI/nVLP-mPhYCM/s1600/QuadraticFormula.JPG

Answer 5

No you just use the quadratic equation :)

Answer 6

\[\large \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\]

Answer 7

Where a,b and c are the coefficients of your equation

a = -16
b = 22
c = 3

Answer 8

okay so...
(-22) + 22^2 - 4 x (-16) x 3
/2 x -16?

Answer 9

\[\large \frac{-22 \pm \sqrt{22^2 - 4(-16)(3)}}{2(-16)}\]

Answer 10

\[\large \frac{-22 \pm \sqrt{484 - (-192)}}{-32}\]

Answer 11

\[\large \frac{-22 \pm \sqrt{676}}{-32}\]

Then can be broken into 2 equations...

\[\large \frac{-22 + \sqrt{676}}{-32}\]
and
\[\large \frac{-22 - \sqrt{676}}{-32}\]

Then solve them

Answer 12

(-22 + 26)/(-32)?
(-22 - 26)/(-32)?

Answer 13

Correct...and completely simplified...?

Answer 14

4/(-32) = -.125
(-48)/(-32) = 1.5?
that sounds wrong...

Answer 15

If it sound wrong lets check it...

\[\large 0 = -16x^2 + 22x + 3\]

lets try -.125 first

\[\large 0 = -16(-.125)^2 + 22(-.125) + 3\]
\[\large 0 = -.25 - 2.75 + 3\]
\[\large 0 = -3 + 3\]
\[\large 0 = 0\] \(\large \color \red{\checkmark}\)

Answer 16

Want to check the other?

Answer 17

I think i should be able to do it by my self :)
thanks man!

Answer 18

No problem bro

Answer 19

yo @johnweldon1993 can you help me with like 2 more parts? they easier...

Answer 20

Sure what do you need man

Answer 21

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.

Answer 22

\[\large \text{Vertex} = -\frac{b}{2a}\]

Answer 23

so thats:
22/2(-16)

Answer 24

close, notice the '-' sign in front

\[\large V = -\frac{22}{2(-16)}\]

Answer 25

ohh i see...

Answer 26

So that is \[\large \frac{-22}{-32} = \frac{11}{16}\]

This is the 'x' coordinate of our vertex

to solve for the 'y' coordinate...you plug in 11/16 into the original equation for 'x'

Answer 27

so now we plug 11/16 in and find the points right?

Answer 28

Correct...you want to find out the 'y' value of the vertex as well...

Answer 29

so 11/16 = .68
f(x) = -16(.68)^2 + 22(.68) + 3

Answer 30

Well don't round it off just yet...you do that afterwards...

11/16 = .6875

\[\large y = -16(.6875)^2 + 22(.6875) + 3\]

Answer 31

thats it? thanks!

Answer 32

would that answer this also?
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.

Answer 33

Well hang on what do you get?

Answer 34

So we get

x = .6875
y = 10.56

right?

now tell me is that a minimum of maximum?

Answer 35

y = -16(.6875)^2 + 22(.6875) + 3
y = -16(.47) + 22 (.6875) + 3
y = -7.52 + 15.125

Answer 36

y = -7.52 + 15.125 + 3
y = -7.52 + 18.125
y = 10.606?

Answer 37

Well yeah there was some rounding error there but regardless yes...

so that is your y-coordinate.....is your vertex a minimum or a maximum?

*hint* it's an upside down parabola thanks to that -16 in front*

Answer 38

Hmm i think its a minimum...am i right?

Answer 39

Not quite...upside down parabola



looks to be the maximum point on that parabola right?

Answer 40

Oh yesh it does look that way...

Answer 41

And to answer that last part you asked...how would you graph f(x)

Well you would mark your 2 x-intercepts...and go up to the maximum that you found....hence...your upside down parabola

Answer 42

Thanks man!

Answer 43

No prob!

Answer 44

I wish i could give you more than a medal n fan because you really helped me!

Answer 45

Don't worry about it man