Unit 2 - Quadratics

Question 1

factor a² - b² - what are the factors called? what method is this?

Answer 1

(a-b)(a+b) - these are conjugates and the method is difference of squares

Question 2

what do you write if it has no factors?

Answer 2

Prime. Also please don’t unless you’ve tried absolutely everything. Including imaginary solutions.

Question 3

What is the zero product property?

Answer 3

If A and B are both real or algebraic expressions, if AB = 0, A or B = 0 (at least one - could be both)

Question 4

What is the domain of a quadratic function?

Answer 4

set of real numbers, (negative infinity, infinity)

Question 5

When |a| < 1, does the graph get thiccer or thinner (wider or narrower)

Answer 5

thiccer and wider - a smol = thicc graph

Question 6

Standard form of a parabola

Answer 6

y = ax² + bx + c

Question 7

Factored/intercept form of a parabola

Answer 7

y=a(x-p)(x-q)

Question 8

Vertex form of a parabola

Answer 8

y=a(x-h)²+k

Question 9

Y intercept of standard form parabola

Answer 9

0, f(0)

Question 10

x intercepts of a standard form parabola

Answer 10

you gotta factor that spit to get there - no easy peasy formula

Question 11

Axis of symmetry of a standard form parabola

Answer 11

-b/2a

Question 12

Vertex of a standard form parabola

Answer 12

-b/2a, f(-b/2a)

Question 13

Range of a standard form parabola

Answer 13

consider y coord of vertex and sign of a, then make a decision

Question 14

y intercept of a factored form parabola

Answer 14

0, f(0)

Question 15

x intercepts of a factored form parabola

Answer 15

(p,0) and (q,0) (please remember to make the sign correct)

Question 16

AoS of a factored form parabola

Answer 16

(p+q)/2
(find the average/midpoint between x intercepts)

Question 17

Vertex of a factored form parabola

Answer 17

p+q … p+q
____ , f( _______)
2 … 2

Question 18

y intercept of a vertex form parabola

Answer 18

0, f(0)

Question 19

x intercepts of a vertex form parabola

Answer 19

this is very annoying because it’s very sneaky about x intercepts and will not tell you in a simple la dee da formula way

Question 20

axis of symmetry in a vertex form parabola

Answer 20

h (NOT K FOR THE LOVE OF GOD)

Question 21

vertex of a vertex form parabola

Answer 21

(h,k) that’s why it’s called vertex

Question 22

how do you convert vertex form to standard form?

Answer 22

square whatever’s in the parentheses
distribute a
add k
add it all up

Question 23

how do you convert vertex form into factored form?

Answer 23

by putting it into standard form
and then factoring because math would like to give me a personal f u

Question 24

If the vertex is (2,4) and a point is (1,3), write a parabola in vertex form that contains those points.

Answer 24

y=a(x-2)²+4
3=a(1-2)²+4
3=a+4
a=-1
y=-(x-2)²+4

Question 25

What is i?

Answer 25

square root of negative 1

Question 26

what is the standard form of a complex number?

Answer 26

a+bi
4+5i
4/5 + 3/5 i (don’t use diagonal fractions or Ms. Cooley will breathe fire)

Question 27

what is sqrt -7 squared?

Answer 27

-7! NOT 7.

Question 28

x²/8 = -4

Answer 28

x² = -32
x = + or -/-32 (it’s the best thing i have)
x = + or - 4i/2

Question 29

what is the complex conjugate of a + bi?

Answer 29

a - bi

Question 30

What is the power order of i?

Answer 30

i if R1, -1 if R2, -i if R3, 1 if no R (r4)

Question 31

what is the reciprocal of a complex number like -6i?

Answer 31

1/-6i but you must rationalize so multiply by 6i/6i and get 6i/-36i² or 6i/36 or i/6

Question 32

What is the first step of completing the square?

Answer 32

move c to the other side
ax²+bx+c=0 –> ax²+bx=-c

Question 33

what is the second step of completing the square?

Answer 33

take half of b and square it and add it to both sides of the equation
ax² + bx + 0.5b² = -c + 0.5b²

Question 34

what is the 3rd step of completing the square?

Answer 34

factor the polynomial on the right because now it will do so easily and simplify the left
(assume a is a square number - if not just root it)(here i’m using a=1 and b=2 and c=10)
(x+1)² = -9

Question 35

what is the fourth step of completing the square?

Answer 35

sqrt both sides
/(x+1) = + or - /-9

Question 36

what is the fifth step of completing the square?

Answer 36

solve for x
x+1 = + or - 3i
x = 1+3i or 1-3i

Question 37

what is the 6th step of completing the square?

Answer 37

marvel at your genius solutions. idk it’s obsolete ok

Question 38

what makes a quadratic good for completing the square?

Answer 38

1 (or at least a square number) = a and b = even but it works regardless

Question 39

what is the discriminant of a quadratic equation?

Answer 39

b²-4ac

Question 40

if the discriminant is positive, the quadratic has __ real solutions

Answer 40

2

Question 41

if the discriminant is negative, the quadratic has __ real solutions

Answer 41

0

Question 42

if the discriminant is 0, the quadratic has __ real solutions

Answer 42

1

Question 43

sum of quadratic equation roots

Answer 43

-b/a

Question 44

product of quadratic equation roots

Answer 44

c/a

Question 45

if given the roots of a quadratic equation, how many possible parabolas could there be?

Answer 45

infinite. just go with a=1 to make your life easier. change it if you need to.

Question 46

if you complete the square for ax squared + bx + c, what do you get?

Answer 46

quadratic formula (i definitely derived it myself without help from mr lee)