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Mathematics
OpenStudy (anonymous):

What is the range of the graph of y = (x - 4)^2 + 3

jimthompson5910 (jim_thompson5910):

Hint: In general, the range of y = a(x-h)^2+k is [k, infinity) if a > 0

OpenStudy (anonymous):

Y ≤ 3??

jimthompson5910 (jim_thompson5910):

close, it should be \[\Large y \ge 3\]

OpenStudy (anonymous):

What about this.... 4x^2 + 13x = -3

jimthompson5910 (jim_thompson5910):

You need to complete the square. Do you know how do to that?

OpenStudy (anonymous):

no

OpenStudy (anonymous):

So the answer would be x = -1/4 and x = -3

jimthompson5910 (jim_thompson5910):

you're looking for the range correct?

OpenStudy (anonymous):

No just solving the equation

jimthompson5910 (jim_thompson5910):

oh sry, I thought you were finding the range

jimthompson5910 (jim_thompson5910):

4x^2 + 13x = -3 4x^2 + 13x + 3 = 0 Now use the quadratic formula to solve for x x = (-b+-sqrt(b^2-4ac))/(2a) x = (-(13)+-sqrt((13)^2-4(4)(3)))/(2(4)) x = (-13+-sqrt(169-(48)))/(8) x = (-13+-sqrt(121))/8 x = (-13+sqrt(121))/8 or x = (-13-sqrt(121))/8 x = (-13+11)/8 or x = (-13-11)/8 x = -2/8 or x = -24/8 x = -1/4 or x = -3 So you are correct, nice job

OpenStudy (anonymous):

Thank you thank you! :)

jimthompson5910 (jim_thompson5910):

sure thing

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