anonymous
  • anonymous
find the x intercept of a parabola with vertex (3,-2) and y intercept (0,7)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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amistre64
  • amistre64
(y+2) = (x-3)^2 +7 y = (x-3)^2 +5
amistre64
  • amistre64
1,-6,14 3 +- sqrt(36 - 4(14))/2 ... aint see it happening
amistre64
  • amistre64
yes I do lol.... its right there

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anonymous
  • anonymous
write it in this form (x1,y1)(x2,y2)
amistre64
  • amistre64
(y+2) = (x-3)^2 +C y = (x-3)^2 +C -2 C-2 = 7; C =9 ........................................ y = (x-3)^2 +9 y = x^2 -6x +9 +9; ug, scratch that y = x^2 -6x +7 .............................. 6 +- sqrt(36 -28) sqrt(8)...2sqrt(2) ---------------- = 2 (3 + sqrt(2), 0) (3 - sqrt(2), 0) maybe lol
anonymous
  • anonymous
\[y=a(x-3)^2-2\] and \[7=a(0-3)^2+2\] \[7=9a+2\] \[5=9a\] \[a=\frac{5}{9}\]
anonymous
  • anonymous
yes?
anonymous
  • anonymous
giving \[y=\frac{5}{9}(x-3)^2-2\]
anonymous
  • anonymous
in the (x1,y1) and (x2,y2) form please, i need two intercepts
anonymous
  • anonymous
ok we have the equation for the parabola. finding x- intercepts means setting y = 0 and solve for x.
amistre64
  • amistre64
x^2 -6x + 7 is good
anonymous
  • anonymous
in other words love \[0=\frac{5}{9}(x-3)^2-2\]
amistre64
  • amistre64
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amistre64
  • amistre64
i used 0,7 ; 3,-2 ; 6,7 lol
anonymous
  • anonymous
in the (x1,y1) and (x2,y2) form
anonymous
  • anonymous
please
anonymous
  • anonymous
well x-intercept means \[(x_1,0)\]
amistre64
  • amistre64
already did; (3-sqrt(2),0) and (3+sqrt(2),0)
anonymous
  • anonymous
what equation did you use?
amistre64
  • amistre64
x^2 -6x +7
anonymous
  • anonymous
(y-k)=a(x-h)^2
amistre64
  • amistre64
(y-7)+9 = (x-3)^2 (y+2) = (x-3)^2
anonymous
  • anonymous
boy am i dumb. i wrote \[y=a(x-3)^2+2\] when it should have been \[y=a(x-3)^2-2\] and \[7=a(-3)^2-2\] \[7=9a-2\] \[9=9a\] \[a=1\]
amistre64
  • amistre64
:) its ok lol
anonymous
  • anonymous
so equation is \[y=(x-3)^2-2\]
anonymous
  • anonymous
idk how to change it to the two points on the graph, please type it that way
anonymous
  • anonymous
or if you prefer \[y+2=(x-3)^2\]
amistre64
  • amistre64
i posted the points 2 times already...
amistre64
  • amistre64
(3+sqrt(2),0) (3-sqrt(2),0) right?
anonymous
  • anonymous
zeros at \[3\pm \sqrt{2}\]
anonymous
  • anonymous
with the parenthesis? and two different points?
anonymous
  • anonymous
with the parenthesis? and two different points?
anonymous
  • anonymous
by inspection
amistre64
  • amistre64
now that 3 and four times lol
anonymous
  • anonymous
\[(2 -\sqrt{3},0)\] \[(2+\sqrt{3},0)\]
amistre64
  • amistre64
sat lol; that was backwards
anonymous
  • anonymous
are the x-intercepts sorry i slowed you up
anonymous
  • anonymous
oh yes it was! \[(3-\sqrt{2},0)\] \[(3+\sqrt{2},0)\]
anonymous
  • anonymous
please in the form of (x1,y1) and (x2,y2) idk what (2-sqrt of 3, 0( means...
anonymous
  • anonymous
means \[x_1=3-\sqrt{2}\] \[y_1=0\]
amistre64
  • amistre64
it means the the sqrt(2) is an EXACT form of an irrational number that can only be expressed approximately in decimal form; of which we have no way of determining the requirements of since you have given us no parameters to establish them by
anonymous
  • anonymous
and \[x_2=3+\sqrt{2}\] \[y_2=0\]
amistre64
  • amistre64
y = 0 exactly at: x = 3-sqrt(2) AND x= 3-sqrt(2) ; otherwise it doesnt...
amistre64
  • amistre64
lol... make one of those a +sqrt(2)
anonymous
  • anonymous
whats x1 and y1?
amistre64
  • amistre64
x1 = 3-sqrt(2) y1 = 0
anonymous
  • anonymous
its wrong
amistre64
  • amistre64
x1 = 1.414213562373095048801688724209.... no, its right; you simply havent given us a means to approximate the answer.
amistre64
  • amistre64
its like saying; what color is the sky? blue. wrong, its a shade of blue that is determined by whatever the criteria is for saying 'blue' in a way that is acceptable...
amistre64
  • amistre64
how old am I ? the right answer depends on how accurate of an answer you want right?

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