Question

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)

Answer 1

plz help

Answer 2

which part?

Answer 3

part b finding the vertex

Answer 4

you know that this graph represents a parabola?

Answer 5

yes but i dont know how to find the vertex without using a graph

Answer 6

for the vertex of the parabola, it has to reach a maxima or a minima. can you tell me what to do to find out the point where the graph reaches its maxima or minima?

Answer 7

no i donk know how to find that. ik that it is a minimum but thats it. is their a formula i can use

Answer 8

i think it is a maxima, but let's get there later. you know how to differenciate right?

Answer 9

i think maximum is downwards and has a positive leading coefficient and minimum is upwards and has a negative leading coefficient

Answer 10

i will help you with that later. at first tell me do you know how to differenciate?

Answer 11

no

Answer 12

okay, no problem. at first, let me be clear that this graph will attain maximum as it is downwards, because its co-efficient of leading term is negative

Answer 13

ok

Answer 14

when i graph it it look like its going upwards

Answer 15

now, for maximum, you need to find out where y=f(x)=-16 x^2+ 22x +3 attains maximum.
-16x^2+22x+3=-(4x)^2+2*4x*2.75-(2.75)^2+3+(2.75)^2=10.5625-(4x-2.75)^2
with a little calculation you can reach this step.. tell me if you have understood

Answer 16

ok i get it

Answer 17

i just completed the square adjusted with 16x^2 and 22x

Answer 18

ok

Answer 19

nice! now as you can see, (4x-2.75)^2 is greater than or equal to zero always, so 10.5625-(4x-2.75)^2 will be maximum when 4x-2.75=0, or x=2.75/4
got it?

Answer 20

yes i got it

Answer 21

so, what is the maximum value of f(x)? obviously when 4x-2.75=0, that means x=0.6875
what is the value of f(x) at that point? clearly 10.5625
as you can see the function attains a maximum at (0.6875, 10.5625), it is the vertex

Answer 22

ohh ok so basically you find the maximum point?

Answer 23

yeah, maximum or minimum, depending on the co-efficient of the leading term. if it's positive, the graph is upward, f(x) is has minima, else the opposites

Answer 24

oh ok thank you so much
can u help with part c now

Answer 25

this is what i put
I would graph this equation by seeing what in formation i have. I already know the vertex and the points where it crosses the x axis. We also know that it is going to be an upwards parabola. I can plot all the points and make a rough drawing of how the parabola line would look.

Answer 26

no, this is downward parabola

Answer 27

oh ok
is the rest good

Answer 28

everything else you have said are all correct :) good job!

Answer 29

ok thank you so much

Answer 30

you are welcome :)