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integrated 9 > quadratics > Flashcards

quadratics Flashcards

1
Q

What is the vertex form of a quadratic?

A

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

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2
Q

What is the standard form of a quadratic?

A

f(x)=ax2+bx+c

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3
Q

What is the factored form of the quadratic?

A

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

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4
Q

What do h and k stand for in the vertex form?

A

(h,k) is the vertex

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5
Q

What do p and q stand for in the factored form of a quadratic?

A

x intercepts

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6
Q

What are the x intercepts from f(x)=2(x-3)(x+4)

A

(3,0) (-4,0)

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7
Q

What are the x intercepts from f(x)=(2x-3)(x-1)

A

(1,0) (3/2,0)

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8
Q

What are the x intercepts from f(x)=2x(x-7)

A

(0,0) (7,0)

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9
Q

What are the x intercepts from f(x)=(x+1)(x-2)

A

(-1,0) (2,0)

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10
Q

What does c stand for in standard form?

A

y intercept

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11
Q

What does a tell you in quadratic equations?

A

if it opens up or down, if it skinny or fat

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12
Q

If a is negative, will the graph open up or down?

A

down

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13
Q

If a is positive, will the graph open up or down?

A

up

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14
Q

Give the a, b, c values of the following f(x)=2x2-3x+4

A

a= 2 b= -3 c=4

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15
Q

Give the vertex from the following equation f(x)=2(x+3)2+4

A

(-3,4)

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16
Q

When we see (x-3)^2 how do we distribute the 2?

A

foil

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17
Q

What is the first thing to look for when factoring

A

greatest common factor

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18
Q

When a>1 how do we start to factor?

A

multiply a and c

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19
Q

To factor when a=1, do the numbers multiply to b or c?

A

c

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20
Q

To factor when a=1, do the numbers add to b or c?

A

b

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21
Q

How do you write equations for axis of symmetry

A

x=

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22
Q

How do you find the axis of symmetry from standard form?

A

x= -b/2a

23
Q

How do you find the axis of symmetry from factored form?

A

(p+q)/2

24
Q

How do you find the axis of symmetry from vertex form?

A

h

25
Q

What are the two ways we can find the x intercepts from standard form of a quadratic?

A

quadratic equation, factoring

26
Q

How do you get from factored form to x intercepts?

A

set each ( ) = 0 and solve for x

27
Q

Zero product property

A

If two things are multiplied together to equal 0, one of the multiplied terms must equal 0

28
Q

What is the quadratic equation?

A
29
Q

What form must the equation be in to use the quadratic equation?

A

standard

30
Q

How do we get x intercepts from vertex form?

A

set y=0 and solve for x

31
Q

If we get a square root of a negative number, what does that mean?

A

imaginary x intercepts

32
Q

If asked for roots what are you finding

A

x intercepts

33
Q

If asked for zeros what are you finding?

A

x intercepts

34
Q

If asked for the solutions of ab equation when y=0 what are you finding?

A

x intercepts

35
Q

What is the x value of the vertex?

A

axis of symmetry

36
Q

How do you find the y value of the vertex

A

plug axis of symmetry in for x in the equation

37
Q

if a is positive will the vertex be a maximum or minimum?

A

min

38
Q

if a is negative will the vertex be a maximum or minimum?

A

max

39
Q

What buttons do you press on the calculatorm after you put in the equation to find the max/min

A

2nd Trace

40
Q

Where do you put the cursor when the bottom of teh screen says left bound?

A

to the left of the max/min

41
Q

Where do you put the cursor when the bottom of teh screen says right bound?

A

to the right of the max/min

42
Q

What are the 5 key points needed to graph a quadratic?

A

y intercept, mirror of y intercept, vertex, 2 x intercept (if any)

43
Q

Points mirror across what in a quadratic function?

A

axis of symmetry

44
Q

if you are mirroring the y intercept, what will the value of the mirrored point be?

A

the same as the y intercept

45
Q

How do you find the x value of a mirrored point

A

The mirrored point is the same distance from the axis of symmetry as the original point

46
Q

What is the discriminant?

A

b2-4ac

47
Q

If there are 2 real x intercepts, what do you know about the discriminant?

A

discriminant>0

48
Q

If there are 0 real x intercepts, what do you know about the discriminant?

A

discriminant<0

49
Q

If there are 2 real repeating x intercepts, what do you know about the discriminant?

A

discriminant=0

50
Q

If there is 1 x intercept, what do you know about the discriminant?

A

discriminant=0

51
Q

If the discriminant is<0 what will the graph look like?

A

The parabola will not cross the x axis

52
Q

If the discriminant =0 what will the graph look like?

A

The parabola will touch the x axis, but not cross the x axis

53
Q

If the discriminant =0 what do you know about the vertex?

A

The vertex is the x intercept

integrated 9 (10 decks)

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