Quick Review Before HW Quiz

y=a(x-h) 2 +k form vertex: ( h, k ) axis: x= h Up if a >0,Down if a <0 EX: y=-(x+1) 2 +4 y=-1(x--1) 2 +4 a=-1, h=-1, k=4 v: (-1,4), a: x=-1,down

y=a(x-h) 2 +k form vertex: ( h, k ) axis: x= h Up if a >0,Down if a <0 EX: y=-3(x-(-2)) 2 y=-3(x--2) 2 +0 a=-3, h=-2, k=0 v: (-2,0), a: x=-2,down

x=a(y-k) 2 +h form vertex: ( h, k ) axis: y= k Right if a >0,Left if a <0 EX: x =2(y-2) 2 +4 x=2(y-2) 2 +4 a=2, h=4, k=2 v: (4,2), a: y=2, right

x=a(y-k) 2 +h form vertex: ( h, k ) axis: y= k Right if a >0,Left if a <0 EX: x =-(y+1) 2 x=-1(y--1) 2 +0 a=-1, h=0, k=-1 v: (0,-1), a: y=-1, left

Recall…Graphing a Parabola Step 1) Determine how it opens Step 2) Draw axis of symmetry Step 3) Plot vertex Step 4) Plot one or two more points, reflect & connect

Example: Graph y=(x-3) 2 -4 Step 1) a=1 > 0…opens up Step 2) a=1, h=3, k=-4 Step 3) Vertex: (h,k)=(3,-4) Step 4) xy (4-3) 2 -4=-34 (5-3) 2 -4=0 5

Jumpstart your brain! 5 Questions – 5 points You have 1 minute per question. Good luck.

REMEMBER

READY SET GO!

Show the work! 1) Which equation has a graph that opens downward? a) y=3x 2 -2b) y=2-3x 2 c) x=3y 2 -2d) x=2-3y 2

Show the work! 2) Find the vertex of the parabola with equation y=-2(x-2) 2 +3.

Show the work! 3) Which equation has the an axis of symmetry of y=-4? a) y=-3(x-4) 2 +5b) y=-3(x+4) 2 +5 c) x=-3(y-4) 2 +5 d) x=-3(y+4) 2 +5

Show the work! 4) Which equation matches the graph? a) y=-(x-4) 2 +2 b) y=-(x-2) 2 +4 c) x=-(y-4) 2 +2 d) x=-(y-2) 2 +4

Show the work! 5) What is the vertex of the parabola defined by: x = –7(y + 3) 2 -6?

Pass your quiz forward. Thank you for participating.

8-2 Parabolas-Day 2

Change to standard form… Change y=x 2 +2x+2 to standard form. Complete the square  add (b/2) 2 Isolate where you will complete the square Write squared term Force the - sign

Change to standard form… Change y=2x 2 -12x+19 to standard form. Factor 2 from x terms Isolate where you will Complete the square Write squared term Complete the square

Change to standard form… Change 4x-y 2 =2y+13 to standard form. The y term is squared, so isolate the x term Complete the square Write squared term Divide by 4, force - sign

Change y-3x 2 =24x+50 to standard form Isolate the y term Complete the square Write squared term Force the - sign Factor 3 from the x terms

Graph y-3x 2 =24x+50 … Step 1) a=3 > 0…opens up Step 2) (a=3, h=-4, k=2) Step 3) Vertex=(h,k)=(-4,2) Step 4) xy -3(-3--4) 2 +2=3 -2(-2--4) 2 +2=6

Homework Parabola Worksheet #2 Complete the chart. When graphing, clearly label 5 points (one will be the vertex) and draw the axis of symmetry