Unit 3

Question 1

What do you use to go from STND-VRTX

Answer 1

complete the square

Question 2

what is the first case for completing the square?

Answer 2

two terms

Question 3

complete the square
x^2 - 8x + ? =?

Answer 3

what two numbers add up to 8? 4
what’s 4x4? 16
x^2 - 8x + 16 = (x-4)^2

Question 4

Complete the square
x^2+10x+?=?

Answer 4

what adds up to 10? 5
what’s 5x5? 25
x^2+10x+25= (x+5)^2

Question 5

what do you need for the second case of completing the square?

Answer 5

three terms

Question 6

complete the square
y= x^2 - 8x + 5

Answer 6

what two numbers add up to 8? 4
what’s 4x4? 16
= (x - 4)^2 - 16 + 5
= (x - 4)^2 - 11
v ( 4, -11)

Question 7

complete the square
y= x^2 + 4x - 3

Answer 7

what two numbers add up to 4? 2
what’s 2x2? 4
= (x + 2)^2 - 4 - 3
= (x + 2)^2 - 7
v ( -2, -7)

Question 8

what do you do for the 3rd case of completing the square?

Answer 8

factor “ a “ out

Question 9

complete the square
y= -2x^2 - 20x + 6

Answer 9

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)

Question 10

complete the square
y= 3x^2 + 18x - 3

Answer 10

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)

Question 11

what is quadratic formula= 3( x^2 + 3)^2

Answer 11

                         2a

Question 12

what do you find when using quadratic formula?

Answer 12

the zeros

Question 13

use quadratic formula to solve this equation
2x^2 + 3x -4 =0

Answer 13

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

Question 14

what if the equation does not equal to zero?
ex. -4x - 5x^2 = - 3

Answer 14

we cannot use quadratic formula unless the equation is equal to zero
-5x^2 - 4x + 3=0

Question 15

what is the discriminant formula?

Answer 15

b^2 - 4ac

Question 16

how many “real roots” are there if the equation is positive?

Answer 16

2 real roots
two answers

Question 17

how many “real roots” are there if the equation is a zero

Answer 17

1 real root
1 answer

Question 18

how many “real roots” are there if the equation is negative

Answer 18

no real roots
you cannot take the square root of a negative number. can’t do it, no answer

Question 19

find the number of roots without graphing
x^2 + x - 2=0

Answer 19

D= b^2 - 4ac
= 1^2 - 4 (1)(-2)
= 9
two real roots

Question 20

find the number of roots without graphing
x^2 -4x = -4

Answer 20

x^2 -4x + 4 = 0
D= b^2 -4ac
= (-4)^2 - 4 (1)(4)
= 16 - 16
= 0
1 real root

Question 21

find the number of roots without graphing
3x^2 - x + 2 = 0

Answer 21

D= (-1)^2 -4 (3)(2)
= 1- 24
= - 23
no real roots

Question 22

what are 3 ways of finding the actual roots

Answer 22

1. factoring and solving
2. quadratic formula

Question 23

how do you find the y-int?

Answer 23

f(0)

Question 24

how do you find the vertex?

Answer 24

z, aos, plug
complete the square

Question 25

how do you find the zeros?

Answer 25

factor and solve
quadratic formula

Question 26

find the parts of the parabola
sketch h= - 2x^2 + x + 10

Answer 26

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

Question 27

determine where y= -3x^2 + 6x + 24 is positive, negative, decreasing and increasing

Answer 27

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)