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2020 BC BLOCK ALGEBRA 2 > DECK 4: QUADRATICS part 1 > Flashcards

DECK 4: QUADRATICS part 1 Flashcards

1
Q

Are all quadratics graphs similar?

A

YES.. THEY ALL HAVE THE EXACT SAME SHAPE.. They are simply zoom-ins or zoom-outs of eachother..

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2
Q

Describe what an axis of symmetry is

A

it is where the parabola can fold onto itself. It is the equation of this vertical line, so you write “x = ___” the equaiont is x= - b/2a

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3
Q

Do all quadratic functions have x intercepts?

A

No, some don’t touch the x axis.. These have imaginary roots and a negative discriminant

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4
Q

Do all quadratics have a y intercept?

A

YES… All quadratics have exactly 1 y-intercept.. (c).. if there is no constant term, the y intercept is 0, so the parabola passes through the origin!!!!

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5
Q

Explain what a parabola with no real roots (real zeros) looks like.

A

doesn’t touch x axis

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6
Q

Explain what a parabola with one real root (real zero) looks like.

A

just touches x axis at one spot, the root (the zero), it doesn’t cross it, it bounces off it, called a “double root”, the vertex is on the x axis

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7
Q

Explain what a parabola with two real roots (real zeros) looks like.

A

crosses x axis at those roots, at those x values

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8
Q

What is the MAX or MIN of a quadratic function?

A

it is the y value at the vertex. In vertex form, it’s simply k. In standard form, Plug -b/2a into the function to get y.remember to look at “a”

+ smiles have min..

  • frowns have max.
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9
Q

How do you find the vertex of a parabola in standard form?

A

the x value is always -b/2a .

To get the y value for it, put that x value into the function and solve

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10
Q

How do you graph a parabola in standard form?

A

first graph the Axis of symmetry with dotted line, (x= -b/2a) then make a T table and use that x value to find the vertex and use a couple integers near it to find other points.

LEAVE SPACE FOR ARITHMETIC.

Reflect over the AOS and connect the dots

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11
Q

How do you know if a parabola has a max or minimum by looking at the function in standard form?

A

if “ a” is pos it is smiling, so it has a min.

if ‘a’ is negative then it is frowning, so it has a max

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12
Q

How do you know if a parabola in standard form opens upward (smile) or down (frown)?

A

if “a” is pos it opens up.

if a is negative, it opens down.

Positive people smile,

negative people frown.

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13
Q

How do you know when a parabola is frowning?

A

when “a” is negative

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14
Q

How do you know when a parabola is smiling?

A

when “a” is positive

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15
Q

How do you solve by factoring?

A

get stuff all on one side, factor, set each factor = 0,then solve each linear equation.

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16
Q

What are solutions to (x+8)(x-3) = 0

A

x = { -8, 3} this is not a point on the graph, it is a set of two numbers that make the equation true. They are also the x intercepts of the parabola

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17
Q

What are the roots of a function? (other names?)

A

the zeros,

the x-intercepts,

the solutions,

where the parabola crosses

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18
Q

What are the solutions of a function? (other names)

A

the roots,

the x intercepts,

the zeros

where the parabola crosses the horizontal axis

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19
Q

What are the three forms of a quadratic function?

A

Standard y=ax2+bx+c

Vertex y=a(x-h)2+k

Factored y=a(x+f)(x+g)

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20
Q

What are the three forms of quadratic functions we use?

A

standard, vertex and factored forms

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21
Q

What are the x intercepts of a function? (other names?)

A

the roots,

the zeros,

the solutions

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22
Q

What are the zeros of a function? (other names?)

A

the roots,

the x intercepts,

the solutions,

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23
Q

What are the zeros of y=5(x-3)(2x+1)

A

The zeros are at (3, 0) and (-1/2, 0)

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24
Q

what is difference between (3, -2) and {3, -2}

A

the first is a point on a plane (over 3, down 2) and is in parentheses…

The second set are numbers in braces, so it is simply a set containing two values, 3 and -2. It is not a point on a plane, the order does non matter in braces.

25
Q

What is the solution to:5(x-8)(x+3)=0

A

8 and -3

(this)(that)=0

we want to make x-8=0 and x+3=0

26
Q

What is the discriminant?

A

b2-4ac

(notice there is no sq root on it. It is the stuff under the root)

27
Q

What is the equation of the axis of symmetry?

A

x = -b / 2a

(notice it is an equation of a vertical line)

28
Q

What is the quadratic formula?

A

x = -b +- sqroot b squared - 4ac all over 2a (but in formula)

29
Q

What is the standard form of a quadratic?

A

ax2+bx+c = 0

30
Q

what is the tough thing about quadratics?

A

the fact that they are squared..

We have to undo that x2.

We want to get it linear!!

31
Q

What is the vertex form of a quadratic?

A

f(x) = a(x-h)2 + k

32
Q

What is the zero product property?

(x-4)(x+8)=0

A

(this)(that)=0

(x-4)(x+8)=0

is true when (this)=0 and when (that)=0

is true when (x-4)=0 and when (x+8)=0

this is what we use when solving by factoring.

We set each factor to zero and solve for x

33
Q

When we solve a quadratic by GRAPHING, what do we look for?

A

look for the x intercepts,

these are the roots

(zeros, solutions)

34
Q

where is the vertex located?

A

on the axis of symmetry (highest or lowest point)

35
Q

why are roots called “zeros”

A

because it is where the height is zero; where the y value is zero; they are the x values that make the y=0

36
Q

Why do parabolas look different if they are all similar?

A

Well…. Simply either imagine zooming way in or zooming way out… this method can always get any 2 parabolas to look the same.

37
Q

why is it called a discriminant?

A

because it discriminates between which type of solutions, roots and zeros you will have (2real, one real or imaginary)

38
Q

Thinking of “a” in a quadratic, how would an “a” of 0.02 be different an “a” of 48

A

0.02 is very small, so the parabola would be wide.. (imagine zooming into a distance of 0.02 inches). An larger a, like 48 inches away (4 feet) the parabola would be narrow, like zooming way out, you would be further away so it would look smaller.

39
Q

How do you know when it is a quadratic?

A

when the highest degreed term is the x2 term (quadrus:square)

40
Q

if -8 is a zero then ___ is a factor

A

(x+8)

41
Q

if (-9, 0) is an x intercept, then ___ is a zero (or root)

A

-9

42
Q

If (4,0) is an x intercept, then ____ is a factor

A

(x-4)

43
Q

If (x-7) is a factor then _____ is a zero (or root)

A

7

44
Q

If (x-8) is a factor then ____ is an x intercept.

A

(8,0)

45
Q

If (x+6) is a factor then ____ is a zero (or root)

A

-6

46
Q

If x is a factor, then ___ is a zero

A

0

47
Q

If 12 is a zero, then ___ is an x intercept

A

(12,0)

48
Q

If 9 is a zero then___ is a factor

A

(x-9)

49
Q

What are the x intercepts of this: f(x): x(x-9)(x+4)

A

there are three: 0, 9 and -4

50
Q

If (2x - 1) is a factor, then how do you find the zero?

A

2x-1=0

solve for x

x= 1/2

51
Q

What are the three common forms of quadratic functions?

A

standard form,

vertex form, and

factored form

(factored form can be called zero form or root form)

52
Q

what does the sign of “a” tell us in all forms of quadratics?

A

“+a” smiling (min),

and

“-a” frowning (max)

53
Q

What does sign of “a” tell us in all forms of quadratics?

A

How the function ends on the RIGHT side.. positive goes up, negative goes down.

54
Q

what is a coefficient?

A

the number in front of a variable or variables

55
Q

What is the equation of the axis of symmetry?

A

x = -b / 2a

(notice it is the equation of a vertical line)

(also notice it is hidden in the quadratic formula)

56
Q

When we graph a parabola to solve a quadratic, what do we look for?

A

look for the x intercepts, these are the roots. The zeros, the solutions

57
Q

why are they called “quadratics?”

A

from latin “quadrus” which means SQUARE

58
Q

What is the square root of -1?

A

i

59
Q

What is i*i ?

A

multiplying i (i) gives you -1

2020 BC BLOCK ALGEBRA 2 (5 decks)

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