2. kelsey has a list of functions. pick one of the g(x) functions below and then describe to kelsey the key features of g(x), including the end behavior, y-intercept, and zeros. o g(x) = x3 − x2 − 4x + 4

Answer with explanation:

g(x)=x³-x²-4 x +4

     =x²×(x-1)-4×(x-1)

     = (x²-4)(x-1)

     =(x-2)(x+2)(x-1)

Use the identity ⇒a²-b²=(a-b)(a+b)

So,Zeroes of Cubic function can be obtained by putting g(x)=0

→(x-2)(x+2)(x-1)=0

 → x= 2, -2, 1  

All the three zeroes of Polynomial g(x) are Real.

Put,x=0 to obtain Y intercept.

⇒g(0)=0³-0²-4×0+4

→g(0)=4-----Y intercept

⇒g(x) increases first ,then Decreases and again it increases.

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12