Students will complete selected problems from Unit 4 Summary and Review for unit 4 test.

Shifting down 4 units is done by… Subtracting 4 from the equation. y = x2 – 4 Shifting down 6 units means… Subtract 6 from the equation. y = x2 + 4 – 6 y = x2 – 2

( 0 , 6 ) Maximum means highest point. Minimum means lowest point. Vertex is the point where it turns. ( 0 , 6 )

the fraction is less than one. The number in front of x 2 is… Negative! That means the graph opens… downward! The graph is shifted 8 units up… so the vertex is: ( 0 , 8 ) Both graphs open downward; the first equation is shifted 8 units up; the first graph is wider because… the fraction is less than one. Since the graph opens downward… It has a Maximum!

Remember: A “smaller” number in front of x2, makes the graph shorter… which makes it appear wider! 3 > 2 Taller = Narrower! 5 > 2 Narrower! < 2 Shorter = Wider! Wider!

– 3 9 < < x < < – 4 0 y Domain is input! x-values! – 3 9 < < x – 4 0 Range is output! y-values! < < y

2 (6)2 + 5 2•36 + 5 72 + 5 f(6) = 77 -2 (2)2 – 6 -2 • 4 – 6 – 8 – 6 f(2) = – 14

y = x2 or f(x) = x2 x y -2 4 -1 1 2

5 2 3 1 4 No number in front of x2 means… 1 in front of the variable. The widest graph has… the smallest number/fraction in front of x2. Remember a smaller number makes it shorter… which appears wider! 5 2 3 No number in front of x2 means… 1 in front of the variable. 1 4

The number in front of x2 is… POSITIVE! That means it opens UP! The + 8 means the graph is… Shifted up 8 from the origin! The vertex is… ( 0 , 8 )

subtract 4 from the equation. 3 • (-2)2 – 5 3 • (-1)2 – 5 3 • (0)2 – 5 3 • (1)2 – 5 3 • (2)2 – 5 7 – 2 – 5 Input or x-values: Keeps getting wider! ALL REAL #’s The number in front of x2 is… 3 3 > 1 Taller looks… y-values: y > – 5 Narrower! 4 units down means… subtract 4 from the equation. y = 3x2 – 5 ( 0 , – 5 ) – 4 y = 3x2 – 9

A2 + B2 = C2 5 2 + 12 2 = C 2 25 + 144 = C 2 169 = C 2 C = 169 C = 13 cm

A2 + B2 = C2 8 2 + 20 2 = C 2 64 + 400 = C 2 464 = C 2 C = 464 C = 21.54 ft

The area of the 2 smaller squares… add up to equal the area of the largest square! 12 2 + 25 = Area of M 144 + 25 = Area of M Area of M = 169 cm 2

--- Because the fraction 1/2 is less than 1… the second graph is shorter and looks wider… --- Because of the minus 5 on the second equation… the second graph is 5 units lower… --- Because the numbers in front of x 2 are both positive… both graphs open UPWARDS.

Quadratic Parent Function is… y = x2 --- Because the – 2 is “bigger” than 1… the first graph is “taller” and looks narrower… --- Because of the minus 6 on the first equation… the first graph is 6 units lower… --- Because the numbers in front of x 2 are –2 and 1 … the first graph opens downwards, and the quadratic parent function opens upwards.

--- A Line of symmetry divides an object in half --- Both halves are reflections of each other. --- On a parabola, the line of symmetry is a vertical line… that passes through the vertex. --- The line of symmetry is defined by the x-value of the vertex ordered pair… example: x = 0

--- The vertex of a parabola is the point where… the graph makes a u-turn. --- It changes from going uphill to downhill… or from going downhill to uphill. --- The vertex is either a maximum (highest point) or… minimum (lowest point).

STUDY! STUDY! STUDY! STUDY! Go back and complete the rest of the problems on the review to practice for the test. STUDY! STUDY! STUDY! STUDY!