anonymous
  • anonymous
Find the x-intercepts of the parabola with vertex (-7,45) and y-intercept (0,-200). Write your answer in this form: (x1,y1),(x2,y2). If necessary, round to the nearest hundredth. Use the method of completing the square to write the equation of the given parabola in this form: (y – k) = a(x – h)2 where a ≠ 0, (h,k) is the vertex, and x = h is the axis of symmetry.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
please help
anonymous
  • anonymous
@THEHELPER123
anonymous
  • anonymous
@phi @dan815 @IrishBoy123 @pooja195 @welshfella

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benlindquist
  • benlindquist
find the common denominator
benlindquist
  • benlindquist
wrong person
anonymous
  • anonymous
oh okay
anonymous
  • anonymous
i just dont understand this
phi
  • phi
did you learn the vertex form of an equation for a parabola?
anonymous
  • anonymous
i have notes....let me see
anonymous
  • anonymous
what it says
anonymous
  • anonymous
well its asking for me to complete the square
anonymous
  • anonymous
it confuses me though because they ask it in a different way
anonymous
  • anonymous
@jabez177
jabez177
  • jabez177
@AlexandervonHumboldt2
phi
  • phi
the form is \[ y= a(x-h)^2 + k\] where (h,k) is the vertex they tell you the vertex, so you can replace the h and k with numbers in that formula can you do that ?
anonymous
  • anonymous
ehhh yeh
anonymous
  • anonymous
there are 4 numbers though......
anonymous
  • anonymous
i cant put both h and k in can i? i mean both h and k's i cant
phi
  • phi
the vertex is (-7, 45) that means use h=-7 and k= 45 in the equation y = a(x-h)^2 + k so replace the h and k letters with numbers. what do you get ?
anonymous
  • anonymous
ohh okay let me try
anonymous
  • anonymous
y=a(x-7)^2+45?
phi
  • phi
it should be x - h in this case x- (-7)
anonymous
  • anonymous
im really lost like this is algebra 2 and up. i only know algebra 1 or less.
phi
  • phi
can you fix your equation? it is not x-7
anonymous
  • anonymous
ehh y=a(-7)+45?
phi
  • phi
no, don't get lost. you want a(x-h)^2 + 45 h is -7 can you simplify x - -7 ? minus a minus is plus, remember?
anonymous
  • anonymous
yeah but im not a very mathematical person. all i see are letters ,numbers,and signs
anonymous
  • anonymous
and then my brain goes in 5 different ways
phi
  • phi
examples: 1 - 1 = 0 1- -1 = 1+1= 2
anonymous
  • anonymous
ohh
phi
  • phi
x- -7 is x+7
phi
  • phi
so far you have \[ y= a(x+7)^2 + 45\] they also tell you (0,-200) is on the curve "plug in" x=0 and y= -200 into your equation. what do you get ?
anonymous
  • anonymous
okay so let me do this
anonymous
  • anonymous
im working it out on paper
anonymous
  • anonymous
uhm is it -200=a(0+7)^2+45?
phi
  • phi
yes. now remember order of operations? first do the parens: 0+7
anonymous
  • anonymous
yeah hold on
anonymous
  • anonymous
do i square the -7?
anonymous
  • anonymous
so that would be -200=a(-49)+45?
phi
  • phi
you get -200= a(7)^2 + 45 (it's +7 or just 7) but yes, now do 7*7
anonymous
  • anonymous
which is 49
phi
  • phi
yes uhm is it -200=a(0+7)^2+45? becomes -200 = 49a + 45 now add -45 to both sides
phi
  • phi
like this -200 + -45 = 49a + 45 + -45
anonymous
  • anonymous
oooh yeah okay hold on
anonymous
  • anonymous
is it a=-200/49?
phi
  • phi
go slower. you have the right idea, but you have to be careful -200 + -45 = 49a + 45 + -45 on the left side, what is -200 + -45
anonymous
  • anonymous
-245
phi
  • phi
and on the right side 45 + -45 is 0 so you have -245 = 49a + 0 adding 0 does not do anything so it's just -245= 49a or 49a = -245
phi
  • phi
now you can divide both sides by 49
anonymous
  • anonymous
so divide -245 by 49 and 49 by 49 which will be 1/5
anonymous
  • anonymous
i think...
phi
  • phi
you do \[ \frac{49}{49} a = \frac{-245}{49} \]
anonymous
  • anonymous
yeah i did that so a=5?
phi
  • phi
you mean a= -5 , right ?
anonymous
  • anonymous
oh yeah lol
anonymous
  • anonymous
okay so i have to solve for x and y?
anonymous
  • anonymous
and one point is -5
phi
  • phi
you found a= -5 so the equation of the curve \[ y= a(x+7)^2 + 45 \] is \[ y = -5(x+7)^2 +45\] this equation tells us everything we want to know about the parabola.
anonymous
  • anonymous
oooh so i just plug it in now?
phi
  • phi
They want Find the x-intercepts of the parabola the x-intercepts are the x values when y is 0 in other words, we have to "solve for x" when y is 0: \[ y = -5(x+7)^2 +45\\ -5(x+7)^2 +45=0\] I would first add -45 to both sides
anonymous
  • anonymous
it depens what we are looking for like is it x
anonymous
  • anonymous
okay so its -7 then
phi
  • phi
no, when x is 0, we get the y-intercept. this is harder. we set the y=0 and we have to find the x that makes y zero. we start with \[ -5(x+7)^2 +45 = 0\] now add -45 to both sides
anonymous
  • anonymous
okay well -5+ -45 is 40
anonymous
  • anonymous
oops i mean -50
phi
  • phi
write down the entire equation (including the x stuff!) \[ -5(x+7)^2 +45 + -45= 0+-45\]
anonymous
  • anonymous
okay
phi
  • phi
to review, we start with \[ -5(x+7)^2 +45 = y\] and we set y =0 (this is how to find the x-intercepts) \[ -5(x+7)^2 +45 = 0\] now we add -45 to both sides \[ -5(x+7)^2 = -45 \] next , divide both sides by -5
anonymous
  • anonymous
okay i got 1 and 9
phi
  • phi
you get \[ (x+7)^2 = \frac{-45}{-5} \]
phi
  • phi
or \[ (x+7)^2 = 9\] now take the square root of both sides
anonymous
  • anonymous
square root of both sides?
phi
  • phi
yes. do you know how to do that ?
anonymous
  • anonymous
just 7^2 or 9^2
anonymous
  • anonymous
or what goes into both evenly
anonymous
  • anonymous
ugh i give up
phi
  • phi
square root "undoes" the square in other words you do \[ \sqrt{(x+7)^2} = \sqrt{9} \]
phi
  • phi
and it's worth remembering \[ \sqrt{x^2} = x \] or in this case \[ \sqrt{(x+7)^2}= x+7\]
phi
  • phi
for the square root of 9, what number times itself is 9 ? 3*3 is 9 that means 3 is the square root. or if you are confused, you can use a calculator you get \[ x+7= \pm 3 \] we usually show both -3 and +3 work: -3*-3 is 9 and so is 3*3 = 9
phi
  • phi
we have two different equations: x+7 = -3 and x+7 = 3 solve each one. can you do that ?
anonymous
  • anonymous
yeah
anonymous
  • anonymous
hold on

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