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- anonymous

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)

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- anonymous

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- anonymous

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

that's fine

- anonymous

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

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- anonymous

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

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

All good till here?

- anonymous

sorta then what would you do

- anonymous

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

- SolomonZelman

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

- anonymous

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

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

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

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

- anonymous

yes please

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