Vertical distance in feet Warm up A rocket has been launched from a cliff 100 feet above sea level. The table below gives the height of the rocket in feet above the water at various times in seconds since the launch. Time in Seconds 75 125 225 400 Vertical distance in feet 100 145 80 Write the quadratic model for the table. Predict the height of the rocket at 300 seconds.

Review HW

CCGPS Analytic Geometry Characteristics & Graphs of Quadratics

STANDARD FORM Table Edit Function Start = AOS Step = 1 Arrow up 1 value to double check the y-values repeat around the vertex

VERTEX FORM Table Edit Function Start = h-value Step = 1 Arrow up 1 value to double check the y-values repeat around the vertex

f(x) = a(x – h)2 + k h is TRICKY! If h is POSITIVE then the graph moves LEFT. If h is NEGATIVE then the graph moves RIGHT. Axis of Symmetry: x = h Special Case If x is NEGATIVE inside then the graph reflects across the y-axis and h takes the sign you see. If a is NEGATIVE then the graph reflects across the x-axis. If |a| is less than 1, the graph SHRINKS. If |a| is greater than 1 the graph STRETCHES. If k is POSITIVE then the graph moves UP. If k is NEGATIVE then the graph moves DOWN. Vertex: (h, k)

Graph opens up and the vertex is the minimum value a is positive Graph opens up and the vertex is the minimum value

Graph opens down and the vertex is the maximum value a is negative Graph opens down and the vertex is the maximum value

From L to R, the x-values where stick man slides down (wheee) Interval of Decrease From L to R, the x-values where stick man slides down (wheee) (-, -1) - -1 

From L to R, the x-values where stick man climbs the mountain… Interval of Increase From L to R, the x-values where stick man climbs the mountain… (-1, ) - -1 

These ALL mean the SAME Roots X-intercepts Solutions Zeros

Homework Multiple-Choice