C1

Question 0

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

Answer 0

Maximum turning point

Sad face ^

Question 1

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

Answer 1

Minimum turning point U

Question 2

Vertex

Answer 2

Turning point

A line of symmetry can be drawn

Question 3

Vertex= (1,3)

Line of symmetry?

Answer 3

X=1

Question 4

Discriminant

Answer 4

b^2 - 4ac

Question 5

How to factories a complicated

ax^2 + bx + c

Answer 5

• 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

Question 6

Completing the square

Of x^2 + bx

Answer 6

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

Question 7

Completing the square

Of x^2 + bx +c

Answer 7

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

Question 9

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

Answer 9

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

Question 10

Least value of the square

Vertex

Answer 10

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

Question 10

Vertex

2(x + 1)^2 -3

Answer 10

(-1,-3)

-b,c

Question 11

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

Answer 11

it is the Maximum/minimum of a parabola

Question 12

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

Answer 12

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

Question 13

Quadratic formula

Answer 13

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

Question 14

b^2 -4ac <0

Real roots?

Answer 14

None

Question 15

b^2 -4ac =0

Answer 15

1

Question 16

b^2 -4ac >0

Answer 16

2

Question 17

Equation has one real root solve to find an imbedded letter

Answer 17

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

Question 18

When you square root what does it give

Answer 18

A + and a -

Question 19

The degree of a polynomial

Answer 19

The highest power of x

Question 20

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

Answer 20

1/2 2 -1/3

Question 21

Cubic functions a>0

Answer 21

Progresses from low left to high right

Question 22

Cubic functions a<0

Answer 22

Progresses from high left to low right

Question 23

How to draw a cubic graph

Answer 23

Find the 3 values of x

Find if a is a + or - (a<>0)so you know which direction it travels

Question 24

Circle equation

Answer 24

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

Question 25

Effect of changing a | (X-a)^2

Answer 25

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

Question 26

Effect of changing a | X^2 + c

Answer 26

Up and down (it is the y intercept)

Question 27

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

Answer 27

Y=(x-1)^2 +3

Question 28

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

Answer 28

Translate by (2/-1)

Question 29

What is the translation of a graph

Answer 29

The same as its vertex

Question 30

Lines are perpendicular if

Answer 30

Both gradients multiplied =-1 m1 x m2 = -1

Question 31

Lines are parallel

Answer 31

If gradients are the same m1 = m2

Question 32

The perpendicular line to line with gradient m

Answer 32

-1/m

Question 33

Midpoint of a line

Answer 33

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

Question 34

Distance between two points

Answer 34

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

Question 35

Gradient of a line

Answer 35

AB = y2-y1/x2-x1

Question 36

Y=3x-2 Gradient and y intercept?

Answer 36

Gradient 3 Y intercept (0,-2)

Question 37

Equation of a line using gradient formula

Answer 37

y-y1=m(x-x1)

Question 38

Fining the point of intersection

Answer 38

Simultaneous equations Find x and y

Question 40

Put into form ax+by+c=0

Answer 40

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

Question 41

a perpendicular line has a

Answer 41

minus reciprocal gradient m becomes -1/m

Question 42

parallel lines have

Answer 42

the same gradient

Question 43

equation of a circle

Answer 43

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

Question 44

equation of a circle center (0,0)

Answer 44

x^2 + y^2 =r^2

Question 45

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

Answer 45

radius =5 | center (-3, 4)

Question 46

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

Answer 46

r^2 (and not just r)

Question 47

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

Answer 47

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

Question 48

What is a tangent to a circle

Answer 48

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

Question 49

What is a normal to a circle

Answer 49

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

Question 50

at a stationary point what is dy/dx

Answer 50

0

Question 51

the discriminant

Answer 51

b^2 -4ac

Question 52

b^2-4ac >0

Answer 52

two real roots

Question 53

b^2 -4ac <0

Answer 53

no real roots

Question 54

b^2-4ac =0

Answer 54

one real root

Question 55

the gradient of a line can be found

Answer 55

by differentiation

Question 56

the differentiated form is also called

Answer 56

the derivative

Question 57

the increasing function

Answer 57

dy/dx >0

Question 58

the decreasing function

Answer 58

dy/dx<0

Question 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

Answer 59

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

Question 60

another word for the gradient

Answer 60

rate of change