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
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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
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Completing the square
Of x^2 + bx
(X+b/2)^2 (b/2)^2
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Completing the square
Of x^2 + bx +c
(X+b/2)^2 (b/2)^2 +c
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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
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Least value of the square
Vertex
Make square =0
Put in "when = x"
Whatever it makes is the least value
(X,lv)
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Vertex
2(x + 1)^2 3
(1,3)
(b,c)
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what does the C value of the completed square form show Maximum/minimum of a parabola
it is the Maximum/minimum of a parabola
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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
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Quadratic formula
(b+ /b^2 4ac) /2a
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b^2 4ac <0
Real roots?
None
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b^2 4ac =0
1
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b^2 4ac >0
2
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Equation has one real root solve to find an imbedded letter
One real root so =0
b^2 4ac
Solve to find letter
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When you square root what does it give
A + and a 
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The degree of a polynomial
The highest power of x
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Roots of f(x)=(2x1)(x2)(3x+1)
1/2 2 1/3
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Cubic functions a>0
Progresses from low left to high right
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Cubic functions a<0
Progresses from high left to low right
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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
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Circle equation
X^2 + y^2 =r^2
(Xa)^2 + (yb)^2 =r^2
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Effect of changing a
(Xa)^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
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Effect of changing a
X^2 + c
Up and down (it is the y intercept)
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translation (1/3) is applied to y=x^2
Outcome
Y=(x1)^2 +3
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Sketch the circle (x2)^2 + (y+1)^2 =4
Translate by (2/1)
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What is the translation of a graph
The same as its vertex
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Lines are perpendicular if
Both gradients multiplied =1
m1 x m2 = 1
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Lines are parallel
If gradients are the same
m1 = m2
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The perpendicular line to line with gradient m
1/m
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Midpoint of a line
(X1+X2/2 ,y1+y2/2)
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Distance between two points
AB =sqrt((x2x1)^2 + (y2y1)^2)
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Gradient of a line
AB = y2y1/x2x1
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Y=3x2
Gradient and y intercept?
Gradient 3
Y intercept (0,2)
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Equation of a line using gradient formula
yy1=m(xx1)
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Fining the point of intersection
Simultaneous equations
Find x and y
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Put into form ax+by+c=0
Rearrange
Multiply by fraction denominators
Write as y=mx+c
Divide by coefficient of y
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a perpendicular line has a
minus reciprocal gradient m becomes 1/m
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parallel lines have
the same gradient
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equation of a circle
(xa)^2 + (yb)^2 =r^2
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equation of a circle center (0,0)
x^2 + y^2 =r^2
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find the radius and center of circle
(x+3)^2 + (y4)^2 25
radius =5
center (3, 4)
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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)
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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
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What is a tangent to a circle
a line on the outside, touches the circle edge once (has one root)
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What is a normal to a circle
Line crossing through the Circle, is the normal to a tangent so splits the circle in half
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at a stationary point what is dy/dx
0
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the discriminant
b^2 4ac
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b^24ac >0
two real roots
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b^2 4ac <0
no real roots
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b^24ac =0
one real root
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the gradient of a line can be found
by differentiation
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the differentiated form is also called
the derivative
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the increasing function
dy/dx >0
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the decreasing function
dy/dx<0
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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
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