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)
Stacey Warren - Expert brainly.com
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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
Okay, f(x) or y both are one and same thing, so you have :
\(y = -16x^2 + 22x + 3\)
Not the answer you are looking for? Search for more explanations.
See, to find x-intercept, you put y = 0..
And to find y-intercept (if someone asks you to), then you put x = 0..
So, here you need to find x-intercept, so you put y = 0, so you have:
\(y = -16x^2 + 22x + 3\)
\(\implies 0 = -16x^2 + 22x + 3\)
All good till here?
sorta then what would you do
Then now you have got a quadratic equation to solve, solve for x there..
the vertex is:
maximum with negative leading coefficient.
minimum with positive leading coefficient.
to find the vertex, complete the square.
Actually, x-intercept is the point where your graph cuts x-axis, and on x-axis, you have only x values, there y = 0..
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..
told part B already....
For part C:
Use the x-intercepts
(you can also use the y-intercept which is simple to find -- optional)
\("\)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.
Do you want to tell me right now, if your vertex is maximum or minimum ?