Unit 3 Flashcards
What do you use to go from STND-VRTX
complete the square
what is the first case for completing the square?
two terms
complete the square
x^2 - 8x + ? =?
what two numbers add up to 8? 4
what’s 4x4? 16
x^2 - 8x + 16 = (x-4)^2
Complete the square
x^2+10x+?=?
what adds up to 10? 5
what’s 5x5? 25
x^2+10x+25= (x+5)^2
what do you need for the second case of completing the square?
three terms
complete the square
y= x^2 - 8x + 5
what two numbers add up to 8? 4
what’s 4x4? 16
= (x - 4)^2 - 16 + 5
= (x - 4)^2 - 11
v ( 4, -11)
complete the square
y= x^2 + 4x - 3
what two numbers add up to 4? 2
what’s 2x2? 4
= (x + 2)^2 - 4 - 3
= (x + 2)^2 - 7
v ( -2, -7)
what do you do for the 3rd case of completing the square?
factor “ a “ out
complete the square
y= -2x^2 - 20x + 6
factor the 2 out
-2 ( x^2 + 10x ) +6
what 2 numbers add up to 10? 5
what’s 5x5? 25
= -2 ( x^2 + 10x + 25 - 25) +6
multiply -25 by -2 to bring it out of the bracket
= -2(x + 5)^2 + 50 + 6
= -2(x + 5)^2 + 56
v (-5, 56)
complete the square
y= 3x^2 + 18x - 3
factor the three out
= 3 (x^2 + 6x)
what two numbers add up to 6? 3
what’s 3x3? 9
= 3 (x^2 + 6x + 9 - 9) -3
multiple -9 by 3 to bring it out of the bracket
= 3( x^2 + 3)^2 - 27 - 3
= 3( x^2 + 3)^2 - 30
v(-3, -30)
what is quadratic formula= 3( x^2 + 3)^2
2a
what do you find when using quadratic formula?
the zeros
use quadratic formula to solve this equation
2x^2 + 3x -4 =0
a=2 b=3 c=4
solve equation in the square root and under the fraction
for for both -3+ and -3-
x= -2.35
x=0.85
what if the equation does not equal to zero?
ex. -4x - 5x^2 = - 3
we cannot use quadratic formula unless the equation is equal to zero
-5x^2 - 4x + 3=0
what is the discriminant formula?
b^2 - 4ac
how many “real roots” are there if the equation is positive?
2 real roots
two answers
how many “real roots” are there if the equation is a zero
1 real root
1 answer
how many “real roots” are there if the equation is negative
no real roots
you cannot take the square root of a negative number. can’t do it, no answer
find the number of roots without graphing
x^2 + x - 2=0
D= b^2 - 4ac
= 1^2 - 4 (1)(-2)
= 9
two real roots
find the number of roots without graphing
x^2 -4x = -4
x^2 -4x + 4 = 0
D= b^2 -4ac
= (-4)^2 - 4 (1)(4)
= 16 - 16
= 0
1 real root
find the number of roots without graphing
3x^2 - x + 2 = 0
D= (-1)^2 -4 (3)(2)
= 1- 24
= - 23
no real roots
what are 3 ways of finding the actual roots
- factoring and solving
- quadratic formula
how do you find the y-int?
f(0)
how do you find the vertex?
z, aos, plug
complete the square
how do you find the zeros?
factor and solve
quadratic formula
find the parts of the parabola
sketch h= - 2x^2 + x + 10
sketch h= - 2x^2 + x + 10
y-int = f(0)
= 10
zeros= = - (2x - 5) (x + 2)
x= 5/2 OR 2.5 x= -2
AOS x= 2.5 + (-2)
——————
2 = 0.25
PLUG f(0.25)= - 2 (0.25)^2 + (0.25) + 10
= 10.125
determine where y= -3x^2 + 6x + 24 is positive, negative, decreasing and increasing
zeros
y= -3 (x^2 - 2x -8)
= -3 (x - 4) (x +2)
x= 4 x= - 2
vertex
y= -3 (x^2 - 2x +1 -1) + 24 ( multiple -1 out by -3)
= -3 (X - 1)^2 + 3 + 24
= -3 (X-1)^2 + 27
V (1,27)