Parabolas,Standard Form,Vertex Form

What direction does a parabola open? with example

1. Look at # in front of x² 2. If # is positive-->UP 3. If # is negative-->DOWN example: -x²+2x-1 The # in front of x² is -1 so it goes DOWN

Steps for Graphing a parabola with example

1. plot the coordinates of the vertex 2. plot the y-intercept 3. look at the y intercept plot. Then plot in the same place on the opposite side of the axis of symmetry. example: y int. plot (1,3) axis of sum (2) other point (3,3)

Finding Coordinates of a Vertex with example

1. solve axis of symmetry 2. plug that # into the equation and solve 3. The axis of symmetry is the x coordinate. Now you solve for the y coordinate. example: f(x)=-x²+2x-1 f(1)=-(1)²+2(1)-1 -1 +2-1=0 x=1 y=0 or (1,0)

Steps to Transform Standard to Vertex Form

1.get terms with "x" to the right of the = 2. take b value, divide it by 2, square it 3. add this # to both sides of the = 4. solve: write in vertex form

Factoring 2 Terms

GCF and Difference of Squares a²-b²=(a+b)(a-b)

AXIS OF SYMMETRY with example

X=-B/2A example: -x2+2x-1 a b c x=-2/2(-1)=-2/-2=1

Example Factoring 2 Terms

example: 4x²-49 1. look for the # that goes into 4 and 49 2. You saw that no numbers go into both 3. Factor out from both #'s factor out 2 from 4 and 7 from 49 because 2x2=4 and 7X7=49 4. When you factor our the numbers you have a 2x left and a 7 left. 5. Your answer is (2x+7)(2x-7) 6. You can check your answer by FOILING it to get your original problem of 4x²-49

Example of Standard to Vertex Form

example: f(x)=3x²-6x-15 step1. f(x)+15=3x²-6x step2. -2/2=-1²=1 step3. f(x)+15+3(1)=3(x²-2x+1) 18=3(x-1)² step4. f(x)=3(x-1)²-18

Factoring 3 terms example

example: x²+11x+30 1. What two numbers mulitply to give you the last number (30) and add to give you the middle numbe (11)? 2. You will find that 5 and 6 add to 11 and multiply to 30. 3. (x+6) (x+5) is your answer 4. You can check your answer by FOILing it to get your original equation