C1 Flashcards
Function f(x)=ax^2 +bx+c
a<0?
-
Maximum turning point
Sad face ^
Function f(x)=ax^2 +bx+c
a>0?
+
Minimum turning point U
Vertex
Turning point
A line of symmetry can be drawn
Vertex= (1,3)
Line of symmetry?
X=1
Discriminant
b^2 - 4ac
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
Completing the square
Of x^2 + bx
(X+b/2)^2 -(b/2)^2
Completing the square
Of x^2 + bx +c
(X+b/2)^2 -(b/2)^2 +c
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
Least value of the square
Vertex
Make square =0
Put in “when = x”
Whatever it makes is the least value
(X,lv)
Vertex
2(x + 1)^2 -3
(-1,-3)
-b,c
what does the C value of the completed square form show Maximum/minimum of a parabola
it is the Maximum/minimum of a parabola
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
Quadratic formula
(-b+- /b^2 -4ac) /2a
b^2 -4ac <0
Real roots?
None
b^2 -4ac =0
1
b^2 -4ac >0
2
Equation has one real root solve to find an imbedded letter
One real root so =0
b^2 -4ac
Solve to find letter
When you square root what does it give
A + and a -
The degree of a polynomial
The highest power of x
Roots of f(x)=(2x-1)(x-2)(3x+1)
1/2 2 -1/3
Cubic functions a>0
Progresses from low left to high right
Cubic functions a<0
Progresses from high left to low right
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