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

1. jim_thompson5910

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

2. lindseyharrison

Y ≤ 3??

3. jim_thompson5910

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

4. lindseyharrison

5. jim_thompson5910

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

6. lindseyharrison

no

7. lindseyharrison

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

8. jim_thompson5910

you're looking for the range correct?

9. lindseyharrison

No just solving the equation

10. jim_thompson5910

oh sry, I thought you were finding the range

11. 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

12. lindseyharrison

Thank you thank you! :)

13. jim_thompson5910

sure thing