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)

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)

anonymous · Answer

I can help with Part A only. :( Is that okay or you need some more talented guy to solve all the three for you? :P

anonymous · Answer

that's fine

anonymous · Answer

Okay, f(x) or y both are one and same thing, so you have :
$y = -16x^2 + 22x + 3$

anonymous · Answer

See, to find x-intercept, you put y = 0..
And to find y-intercept (if someone asks you to), then you put x = 0..

anonymous · Answer

So, here you need to find x-intercept, so you put y = 0, so you have:
$y = -16x^2 + 22x + 3$
$\implies 0 = -16x^2 + 22x + 3$

anonymous · Answer

All good till here?

anonymous · Answer

sorta then what would you do

anonymous · Answer

Then now you have got a quadratic equation to solve, solve for x there..

solomonzelman · Answer

Part B:

the vertex is:

maximum with negative leading coefficient.
minimum with positive leading coefficient.

to find the vertex, complete the square.

anonymous · Answer

Actually, x-intercept is the point where your graph cuts x-axis, and on x-axis, you have only x values, there y = 0..

anonymous · Answer

That is why we put y = 0 to find x-intercept..
@SolomonZelman will tell you the next two parts.
Just solve the quadratic equation to find x..

solomonzelman · Answer

told part B already....
----------------------------------

For part C:

Use the x-intercepts
(you can also use the y-intercept which is simple to find -- optional)

And for
$"$Justify that you can use the answers obtained
in Part A and Part B to draw the graph.$"$

it is justified, but your graph of course won't look and be exact as on a graphing calculator.

solomonzelman · Answer

Do you want to tell me right now, if your vertex is maximum or minimum ?

anonymous · Answer

yes please