Question

I WILLL MEDAL AND FAN!!!
An expression is shown below:
f(x) = -16x^2 + 22x + 3

Part A: What are the x-intercepts of the graph of the f(x)? Show your work.

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.

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.

Answer 1

part A, set
\[-16x^2 + 22x + 3 =0\] and solve for \(x\)

Answer 2

it is not that straight forward, probably have to use the quadratic formula
i would start with
\[16x^2-22x-3=0\] and that one

Answer 3

Quadratic formula:
\[x = \frac{ -b \sqrt{b^{2}-4ac}}{2a }\]

Answer 4

\[x = \frac{ -b\color{red}{\pm} \sqrt{b^{2}-4ac}}{2a }\]

Answer 5

just multiply -16 by 3 = -48

find the factors that add to 22...... 24 - 2

then its

(-16x + 24)(-16x - 2)
-------------------
-16

factoring and you get

8(-2x + 3)-2(8x + 1)
------------------
-16

cancel the common factors

(-2x +3)(8x + 1) = 0

so solve

-2x + 3 = 0

and

8x + 1 = 0

for the intercepts

Answer 6

so for the man or min... look at the sign of the leading term....

Answer 7

So Is It A Maximum?

Answer 8

thats correct...

Answer 9

the vertex.... so it can be found by 1st finding the line of symmetry

in the general form

y = ax^2 + bx + c

the line of symmetry is

\[x = \frac{-b}{2a}\]

in your question b = 22 and a = -16

the vertex is on the line of symmetry...

so substitute the value of x into the original equation to find the vertex...


then you can use A and B to graph the equation...

you know x - intercepts, vertex, concavity and by letting x = 0 you can find the y- intercept...

hope it helps

Answer 10

Thank You So Much Campbell!