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Flashcards in C1 Deck (60):
0

Function f(x)=ax^2 +bx+c
a>0?
+

Minimum turning point U

1

Function f(x)=ax^2 +bx+c
a<0?
-

Maximum turning point
Sad face ^

2

Vertex

Turning point
A line of symmetry can be drawn

3

Vertex= (1,3)
Line of symmetry?

X=1

4

Discriminant

b^2 - 4ac

5

How to factories a complicated
ax^2 + bx + c

-make equation so that a is +
- a X c
-find two factors of ac that when added= b (call these zx and yx)
- (ax^2 +zx)+(yx+c)
- simplify
- delete one of the like brackets make a second bracket from what you removed
-now add - negatives so you get original equation when multiplied

6

Completing the square
Of x^2 + bx

(X+b/2)^2 -(b/2)^2

7

Completing the square
Of x^2 + bx +c

(X+b/2)^2 -(b/2)^2 +c

9

Completing the square
3x^2 + 2x +1
Same if a is a -

3(x^2 +2/3x) +1
3((x+1/3)^2 -(1/3)^2 ) +1
3((x+1/3)^2 -(1/9))+1
3(x+1/3)^2 - 1/3 +1
3(x+1/3)^2 +2/3

10

Least value of the square
Vertex

Make square =0
Put in "when = x"
Whatever it makes is the least value
(X,lv)

10

Vertex
2(x + 1)^2 -3

(-1,-3)

(-b,c)

11

what does the C value of the completed square form show Maximum/minimum of a parabola

it is the Maximum/minimum of a parabola

12

When solving an equation by completing the square what must you not forget

There are two answers
One is +sqr rt
Other is -sqr rt

13

Quadratic formula

(-b+- /b^2 -4ac) /2a

14

b^2 -4ac <0
Real roots?

None

15

b^2 -4ac =0

1

16

b^2 -4ac >0

2

17

Equation has one real root solve to find an imbedded letter

One real root so =0
b^2 -4ac
Solve to find letter

18

When you square root what does it give

A + and a -

19

The degree of a polynomial

The highest power of x

20

Roots of f(x)=(2x-1)(x-2)(3x+1)

1/2 2 -1/3

21

Cubic functions a>0

Progresses from low left to high right

22

Cubic functions a<0

Progresses from high left to low right

23

How to draw a cubic graph

Find the 3 values of x
Find if a is a + or - (a<>0)so you know which direction it travels

24

Circle equation

X^2 + y^2 =r^2

(X-a)^2 + (y-b)^2 =r^2

25

Effect of changing a
(X-a)^2

From side to side
If it is -2 then it will touch x axis at 2
If it is 3 then it will touch x axis at -3

26

Effect of changing a
X^2 + c

Up and down (it is the y intercept)

27

translation (1/3) is applied to y=x^2
Outcome

Y=(x-1)^2 +3

28

Sketch the circle (x-2)^2 + (y+1)^2 =4

Translate by (2/-1)

29

What is the translation of a graph

The same as its vertex

30

Lines are perpendicular if

Both gradients multiplied =-1

m1 x m2 = -1

31

Lines are parallel

If gradients are the same

m1 = m2

32

The perpendicular line to line with gradient m

-1/m

33

Midpoint of a line

(X1+X2/2 ,y1+y2/2)

34

Distance between two points

AB =sqrt((x2-x1)^2 + (y2-y1)^2)

35

Gradient of a line

AB = y2-y1/x2-x1

36

Y=3x-2

Gradient and y intercept?

Gradient 3

Y intercept (0,-2)

37

Equation of a line using gradient formula

y-y1=m(x-x1)

38

Fining the point of intersection

Simultaneous equations

Find x and y

40

Put into form ax+by+c=0

Rearrange
Multiply by fraction denominators
Write as y=mx+c
Divide by coefficient of y

41

a perpendicular line has a

minus reciprocal gradient m becomes -1/m

42

parallel lines have

the same gradient

43

equation of a circle

(x-a)^2 + (y-b)^2 =r^2

44

equation of a circle center (0,0)

x^2 + y^2 =r^2

45

find the radius and center of circle
(x+3)^2 + (y-4)^2 -25

radius =5
center (-3, 4)

46

After completing the square to find the equation of a circle what is the number outside of the brackets

r^2 (and not just r)

47

How do you know if an angle in a circle is a right angle

If it is subtended at the circumference of a circle by a diameter.
An angle in a semicircle is a right angle

48

What is a tangent to a circle

a line on the outside, touches the circle edge once (has one root)

49

What is a normal to a circle

Line crossing through the Circle, is the normal to a tangent so splits the circle in half

50

at a stationary point what is dy/dx

0

51

the discriminant

b^2 -4ac

52

b^2-4ac >0

two real roots

53

b^2 -4ac <0

no real roots

54

b^2-4ac =0

one real root

55

the gradient of a line can be found

by differentiation

56

the differentiated form is also called

the derivative

57

the increasing function

dy/dx >0

58

the decreasing function

dy/dx<0

59

what do you do if you get 0 for d^2/dx^2 when you need to find if it is decreasing or increasing

put in -1, 0, 1 into dy/dx
you can tell what shape the graph is making
min is U max is A

60

another word for the gradient

rate of change