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

Question

jim_thompson5910 · Answer

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

anonymous · Answer

Y ≤ 3??

jim_thompson5910 · Answer

close, it should be $$\Large y \ge 3$$

anonymous · Answer

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

jim_thompson5910 · Answer

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

anonymous · Answer

no

anonymous · Answer

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

jim_thompson5910 · Answer

you're looking for the range correct?

anonymous · Answer

No just solving the equation

jim_thompson5910 · Answer

oh sry, I thought you were finding the range

jim_thompson5910 · Answer

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

anonymous · Answer

Thank you thank you! :)

jim_thompson5910 · Answer

sure thing