Question

find the minimum y-value on the graph of y=f(x) for f(x)=7x^2+7x-4

Answer 1

I have gotten as far as \[7(-\frac{ 1 }{ 2 })^2+7(-\frac{ 1 }{ 2 })-4\] then I get stuck

Answer 2

I know that I have to evaluate \[f(-\frac{ 1 }{ 2 }) \] but I am not sure how to do so

Answer 3

I have gotten the x-value now I just need the y-value

Answer 4

I know the steps on how to do this but for some reason this one has me stuck

Answer 5

Well, what is (-1/2)^2?

Answer 6

wouldnt it be -1

Answer 7

Thats adding them, we want to square it. So (-1/2)*(-1/2)

Answer 8

I dont know then

Answer 9

-1/4

Answer 10

Close. you have to multiply both negatives, too. 2 negatives make a positive.

Answer 11

oh yeah ok so 1/4

Answer 12

Yep. So now 7(-1/2)?

Answer 13

3 1/2?

Answer 14

-7/2

Answer 15

Yep, exactly. So you need to be able to do 7/4 - 7/2 - 4.

Answer 16

and how do I do that

Answer 17

would I make the 4 a 4/1

Answer 18

Well, you would need a common denominator for all of them.

Answer 19

\[\frac{ 7 }{ 4 }-\frac{ 7 }{ 2 }-\frac{ 4 }{ 1 }\]

Answer 20

Thats a start. So what would your common denominator be?

Answer 21

common denominator would be 4

Answer 22

Right. So now do what you need to do to make all of those fractions have a denominator of 4 and then subtract : )

Answer 23

\[\frac{ 7 }{4? }-\frac{ 14 }{ 4 }-\frac{ 16 }{ 4 }\]

Answer 24

sorry didnt mean to leave the ?

Answer 25

Looks fine to me. Now just subtract.

Answer 26

so -23/4

Answer 27

Yep, that would be your y-value :3

Answer 28

ok thanks, I know this stuff but for some reason that one puzzled me

Answer 29

No worries. You get better and better at them :3 Good luck.