Question

Find the value of c that makes the expression a perfect square trinomial. Then write the expression as the square of a binomial.
x^2+7x+c
Please show work because i don't understand it.

Answer 1

answer: 49/4 i think..

Answer 2

Can you show work please??? I think that is the answer but idk how to get it.

Answer 3

because the formula for a perfect square trinomial is a^2+2ab+(b/2)^2???

Answer 4

if you work the answer backward
(x+7/2)(x+7/2)
=x^2+2(7/2)+(7/2)^2
=X^2+7+(49/4)

Answer 5

there is a process called "completing the square" which will give the answer, btw 49/4 is the correct answer.

but the process is this: in the expression\[x^2+bx+c\]the value of c for the poly to be a perfect square trinomial is\[\left( \frac{b}{2} \right)^2\]. in your example b=7, so c needs to be\[\left( \frac{7}{2} \right)^2=\frac{49}{4}\]

Answer 6

btw cool green eye

Answer 7

Thanks, help me with another!!! x^2-13x+c
Same concept?

Answer 8

ok

Answer 9

\[c=\left( \frac{13}{2} \right)^2=\frac{169}{4}\]so the perfect square trinomial expression is\[x^2-13x+\frac{169}{4}\]

Answer 10

add half of the middle coefficient, squared

Answer 11

wow! the server just kicked me off, but i'm back now. as i was trying to say:

this method only works if the first coefficient (the with x^2) is a +1

Answer 12

okay, i think i got it :) I have a word problem, do u think you can help me?

Answer 13

i'll try

Answer 14

Okay you have to use completing the square to find the vertex in the funtion's graph.

Answer 15

ok shoot

Answer 16

When you walk x meters per minute, your rate y of energy use (in calories per minute) can be modeled by y=0.0085x^2-1.5x+120.

Answer 17

\[y=0.0085x^2-1.5x+120\]
we need the leading coefficient to be a 1, and we need to get the 120 on the left side temporarily: first subtract 120, then divide by 0.0085\[\frac{y-120}{0.0085}=x^2-\left( \frac{1.5}{.0085} \right)x\]

Answer 18

now we will multiply the coefficient for the x-term by 1/2 and then square it and add it the right side to make a perfect square trinomial.

Answer 19

here's the catch: this is an equation and if we add this number to the right side, then we must also add it to the left side, right? OR, we can add and subtract it to the right side only. same difference, no?

Answer 20

\[\frac{y-120}{.0085}=x^2-\left( \frac{1.5}{.0085} \right)x+\left( \frac{1}{2}*\frac{1.5}{.0085} \right)^2-\left( \frac{1}{2}*\frac{1.5}{.0085} \right)^2\]the first three terms on the right side is a perfect square trinomial; the subtracted term will (in part) be the y-coordinate of the vertex.

Answer 21

Alright, we can move on ^_^ Yayy! :D

Answer 22

i forgot to take the square root to get the 88.235...\[\frac{y-120}{.0085}\approx(x-88.2353)^2-1767785.467\]now all we have to do is solve for y

Answer 23

i don't know if this happening to anyone else, but i lost my connection to the open study server again; i'm going to finish the problem in hope you'll come to view it :(

Answer 24

the standard form of a quadratic function with vertex (h, k) is\[y=a(x-h)^2+k\]compare this to the equation from your problem and you can see that

h=88.2353 and k=-186.176

Answer 25

to solve for y, you first multiply through by 0.0085\[y-120 \approx 0.0085(x-88.2353)^2-(7785.467*.0085)\]then add 120\[y \approx 0.0085(x-88.2353)^2+53.8235\]now this is in the so-called standard form for a quadratic function from which we can read the vertex: V(88.2353, 53.8235)

Answer 26

the standard form of a quadratic function with vertex (h, k) is\[y=a(x−h)^2+k\]compare this to the equation from your problem and you can see that

h=88.2353 and k=53.8235