Step-by-step explanation:
Equation: y= [tex]-x^2+3x+9[/tex]
To create a parabola:
Does your parabola open up or down: If up, a>0 if down, a<0
This one opens down.
Is there a vertical strech or vertical compression:
No
What is the y-intercept: (0,9)
What strategy: Quadratic formula
Why?: You can fully factor the equation. You just get
-([tex](x^2-3x-9)[/tex] which isn't factorable.
Use the quadratic formula, where a= -1, b= 3, and c=9 to show your work.
Quadratic formula: [tex]\frac{-b+\sqrt{b^2-4ac} }{2a} \frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]
[tex]\frac{-(3)+\sqrt{(3)^2-4(-1)(9)} }{2(-1)}[/tex] and [tex]\frac{-(3)-\sqrt{(3)^2-4(-1)(9)} }{2(-1)}[/tex]
[tex]\frac{-3+\sqrt{9-4(-9)} }{-2}[/tex] and[tex]\frac{-3-\sqrt{9-4(-9)} }{-2}[/tex]
[tex]\frac{-3+\sqrt{9+36} }{-2}[/tex] and [tex]\frac{-3-\sqrt{9+36} }{-2}[/tex]
[tex]\frac{-3+\sqrt{45} }{-2}[/tex] and[tex]\frac{-3-\sqrt{45} }{-2}[/tex]
[tex]\sqrt{45}[/tex] = [tex]\sqrt{9 (5)} = 3\sqrt{5}[/tex]
[tex]\frac{-3+3\sqrt{5} }{-2}[/tex] and [tex]\frac{-3-3\sqrt{5} }{-2}[/tex]
Cancel the negatives (-3) and (-2)
[tex]\frac{3 +3\sqrt{5} }{2} or\frac{3 -3\sqrt{5} }{2}[/tex] = end result
Good luck!
