Question

What is one of the zeros of the function shown in this graph?

Answer 1

zeros are the same as x-intercepts of the function. It is when y=0, so you have points (x,0) .

look at your graph, since it is a quadratic equation you have two zeros. From the hint that I gave you above, can you tell me these points?

Answer 2

(-4,0)?

Answer 3

nope, the graph does not pass through that point
try again

Answer 4

(-1,0)?

Answer 5

make sure that the points are 'INCLUDED' in the graph.

Answer 6

(-3,0) and (1,0)?

Answer 7

yesh

Answer 8

ohh okay could you help me with one more?

Answer 9

i'll try if i still have some time left

Answer 10

I attached the question above

Answer 11

do you know how to calculate for the discriminant?

Answer 12

yes b^2-4ac

Answer 13

ok good. do you know how to apply it?

if the discriminant is equal to zero, what does it mean?
if it is less than zero?
if it is greater than zero?

Answer 14

I know how to plug in the numbers but I dont know the rest of it

Answer 15

if the discriminant is equal to zero, it means that it has ONE zero/root/x-intercept/solution.
if it is less than zero, it means that the root nature of the quadratic equation is NOT REAL (imaginary).
if it is greater than zero, it means that there are TWO real roots/zeros/xints/solutions.

so try calculating for the discriminant of that equation and tell me what is the value of the discriminant.

Answer 16

\[x ^{2}+3x-7=0\]
a=1, b=3, c=-7
\[b ^{2}-4ac\]
\[3^{2}-4(1)(-7)=37\]

Answer 17

is 37 greater than, equal, or lesser than zero?
so what does it mean? (refer to the info that i gave you)

Answer 18

its greater than zero so it has two real roots?

Answer 19

absolutely right ^_^

Answer 20

yay(: thank you(: could I ask you one more question

Answer 21

lol okay

Answer 22

could you help me with this one?

Answer 23

sorry i was doing something.
gimme a sec. i'll look at it.

Answer 24

Oh im sorry to bother you

Answer 25

no its okay :)

so we are looking for the maximum point of this quadratic equation.
do you know how to find the vertex(h,k)?

Answer 26

vertex formula?

Answer 27

yes or change the standard form into vertex form?

Answer 28

Im not good at changing formulas

Answer 29

alright, let's just use the vertex formula. its easier

\(\Large (h,k) = (\frac{-b}{2a},k) = (x, r(x))\)

we are solving for k or r(x)

Answer 30

\(r(x)=10x-0.025x^2\)

\(a\)= -0.025, \(b\)=10 plug into the formula \(\Large \frac{-b}{2a}\) to solve for the number of toys (\(x\)), when the revenue is at the maximum.

then after you find \(x\) or the number of toys, substitute it in the original equation \(r(x)=10x-0.025x^2\), to solve for the maximum revenue.

Answer 31

i finished calculating it, what did you get?

Answer 32

\[\frac{ -b }{ 2a }=\frac{ -10 }{ 2*0.025 }=200\]
\[r(200)=10*(200)-0.025*(200)^{2}=1000\]

Answer 33

also remember that question says that the revenue is 'measured in thousands of dollars', so multiply your answer, which is right btw, by $1000

Answer 34

oops i meant -200

Answer 35

so it would be -1000

Answer 36

no, the first one is right because you substitute \(0.025\) instead of \(-0.025\), so you should end up having a POSITIVE answer

Answer 37

i mean the answer should be positive

Answer 38

Ohh okay so then it would be 1,000,000?

Answer 39

yep

Answer 40

dont forget the unit

Answer 41

therefore, your answer should be $1,000,000

Answer 42

Okay thank you(:

Answer 43

no problem :)