You can use the <u>determinant</u><u> (square root)</u> of a quadratic equation to determine the number and type of solutions of the equation.
> 0 → 2 real solutions
= 0 → 1 real solution (double root)
< 0 → 2 imaginary(complex) solutions
Answer:
Graph = Cardioid
Axis of symmetry = y-axis
Critical points=
Step-by-step explanation:
General equation for this type of cardioid is:
a ± b sinθ
Condition for a cardioid =
Axis of symmerty according to the graph of 2 + 2 sinθ is along y-axis.
Critical points:
r = 2 + 2 sinθ ⇒ r = 2(1 + sinθ) ⇒ r' = 2 cosθ
∵derivative of 1 + sinθ = cosθ
For finding critical point the derivative is equal to zero,
2 cosθ = 0 ⇒ cosθ = 0
the value of cosθ is equal to zero at intervals:
So, critical points =
