EOC TEST STRATEGIES QUADRATICS FINDING ZEROES ZEROES KEY

EOC TEST STRATEGIES: QUADRATICS: FINDING ZEROES

ZEROES KEY TERMS • ROOTS METHODS TO FIND • FACTOR, SET = TO 0 & SOLVE. • ZEROES • “HIT THE GROUND” • RETURN TO ZERO • “BREAK EVEN” • SOLUTIONS • USE CALCULATOR

WE WILL LOOK AT 3 DIFFERENT WAYS TO FIND ZEROES • FACTORING • CALCULATOR TABLE • CALCULATOR TRACE

EXAMPLE Q 2. 1 - USING FACTORING SUPPOSE THE EQUATION H(T) = -T 2 + 5 T + 14 MODELS THE HEIGHT OF A BALL THROWN INTO THE AIR OFF THE TOP OF THE BLEACHERS. HOW MANY SECONDS DOES IT TAKE FOR THE BALL TO HIT THE GROUND? -T 2 + 5 T + 14 -1(T 2 - 5 T – 14) -1(T – 7) (T + 2) T-7=0 T+2=0 T=7 T = -2 ANSWER ______

EXAMPLE Q 2. 1 - USING CALCULATOR TABLE • FIRST – TYPE EQUATION IN “Y=“ SUPPOSE THE EQUATION H(T) = T 2 + 5 T + 14 MODELS THE HEIGHT OF A BALL THROWN INTO THE AIR OFF THE TOP OF THE BLEACHERS. • THEN – GO TO HOW MANY SECONDS DOES IT “ 2 ND” “TABLE” TAKE FOR THE BALL TO HIT THE AND PAGE UP/DOWN TO GROUND? SEE THE WHERE Y = 0. ANSWER ______

EXAMPLE Q 2. 1 - USING CALCULATOR TRACE • ARROW UNTIL THE CURSOR IS ABOVE THE LINE & HIT & “ENTER” • FIRST – TYPE EQUATION IN “Y=“ • THEN – “ 2 ND” “TRACE” • NEXT – CHOOSE #2 “ZERO” “ENTER” • ARROW UNTIL THE CURSOR IS BELOW THE LINE & HIT & “ENTER” • “ENTER” ONCE MORE WHEN IT SAYS ‘GUESS? ’ ZERO

CHECK IT: Q#2. 2 • THE WEEKLY SALES OF A NEW SCHOOL SHIRT AFTER X WEEKS IS MODELED BY THE FUNCTION P(X) = -3 X 2 + 2 X + 40. AFTER HOW MANY WEEKS DO THE SALES HIT ZERO?

CHECK IT Q 2. 3 • A BALL IS THROWN INTO THE AIR WITH A SPEED OF 32 FEET PER SECOND. THE FUNCTION H = 32 T – 16 T 2 MODELS THE HEIGHT OF THE BALL AFTER T SECONDS. FOR HOW MANY SECONDS WAS THE BALL IN THE AIR?

CHECK IT Q 2. 4 • A CLUB IS MAKING DECORATIVE WREATHS. ITS DAILY COST CAN BE MODELED WITH THE FUNCTION P(X)=3 X 2 – 24 X, WHERE X IS THE NUMBER OF WREATHS PRODUCED. HOW MANY WREATHS NEED TO BE PRODUCED FOR THE CLUB TO BREAK EVEN? (PROFIT = 0)

CHECK IT Q 2. 5 • JENNY USED THE EXPRESSION -16 X 2 + 38 X + 5 TO DETERMINE THE HEIGHT OF AN OBJECT X SECONDS AFTER IT WAS HIT INTO THE AIR. WRITE AN INEQUALITY TO REPRESENT THE INTERVAL OF TIME THAT THE OBJECT WAS IN THE AIR.

CHECK IT Q 2. 6 • IDENTIFY THE ROOTS FOR THE FUNCTION F(X) = 2 X 2 – 3 X – 9.