Unit 2 - Quadratics Flashcards

1
Q

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

A

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

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2
Q

what do you write if it has no factors?

A

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

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3
Q

What is the zero product property?

A

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

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4
Q

What is the domain of a quadratic function?

A

set of real numbers, (negative infinity, infinity)

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5
Q

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

A

thiccer and wider - a smol = thicc graph

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6
Q

Standard form of a parabola

A

y = ax² + bx + c

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7
Q

Factored/intercept form of a parabola

A

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

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8
Q

Vertex form of a parabola

A

y=a(x-h)²+k

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9
Q

Y intercept of standard form parabola

A

0, f(0)

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10
Q

x intercepts of a standard form parabola

A

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

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11
Q

Axis of symmetry of a standard form parabola

A

-b/2a

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12
Q

Vertex of a standard form parabola

A

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

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13
Q

Range of a standard form parabola

A

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

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14
Q

y intercept of a factored form parabola

A

0, f(0)

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15
Q

x intercepts of a factored form parabola

A

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

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16
Q

AoS of a factored form parabola

A

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

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17
Q

Vertex of a factored form parabola

A

p+q … p+q
____ , f( _______)
2 … 2

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18
Q

y intercept of a vertex form parabola

A

0, f(0)

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19
Q

x intercepts of a vertex form parabola

A

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

20
Q

axis of symmetry in a vertex form parabola

A

h (NOT K FOR THE LOVE OF GOD)

21
Q

vertex of a vertex form parabola

A

(h,k) that’s why it’s called vertex

22
Q

how do you convert vertex form to standard form?

A

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

23
Q

how do you convert vertex form into factored form?

A

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

24
Q

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

A

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

25
What is i?
square root of negative 1
26
what is the standard form of a complex number?
a+bi 4+5i 4/5 + 3/5 i (don't use diagonal fractions or Ms. Cooley will breathe fire)
27
what is sqrt -7 squared?
-7! NOT 7.
28
x²/8 = -4
x² = -32 x = + or -/-32 (it's the best thing i have) x = + or - 4i/2
29
what is the complex conjugate of a + bi?
a - bi
30
What is the power order of i?
i if R1, -1 if R2, -i if R3, 1 if no R (r4)
31
what is the reciprocal of a complex number like -6i?
1/-6i but you must rationalize so multiply by 6i/6i and get 6i/-36i² or 6i/36 or i/6
32
What is the first step of completing the square?
move c to the other side ax²+bx+c=0 --> ax²+bx=-c
33
what is the second step of completing the square?
take half of b and square it and add it to both sides of the equation ax² + bx + 0.5b² = -c + 0.5b²
34
what is the 3rd step of completing the square?
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
35
what is the fourth step of completing the square?
sqrt both sides /(x+1) = + or - /-9
36
what is the fifth step of completing the square?
solve for x x+1 = + or - 3i x = 1+3i or 1-3i
37
what is the 6th step of completing the square?
marvel at your genius solutions. idk it's obsolete ok
38
what makes a quadratic good for completing the square?
1 (or at least a square number) = a and b = even but it works regardless
39
what is the discriminant of a quadratic equation?
b²-4ac
40
if the discriminant is positive, the quadratic has __ real solutions
2
41
if the discriminant is negative, the quadratic has __ real solutions
0
42
if the discriminant is 0, the quadratic has __ real solutions
1
43
sum of quadratic equation roots
-b/a
44
product of quadratic equation roots
c/a
45
if given the roots of a quadratic equation, how many possible parabolas could there be?
infinite. just go with a=1 to make your life easier. change it if you need to.
46
if you complete the square for ax squared + bx + c, what do you get?
quadratic formula (i definitely derived it myself without help from mr lee)