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IB topic 2 - Chapter 3
What does a trinomial look like?
Ax² + bc +c
2 types of factoring trinomials - Think: what do you look for first?
1) when a = 1, you can just distribute factors of AC that are the sum of B
2) when a > 1, you need to split b (with the 2 factors) but still enter into the trinomial. Then look for the GCF from the new split equation (writhing the trinomial) - from their you should have 2 () that are the same - and create your second () out of the GCF’s you placed on the outside
Gradient
IB term for slope (still = m)
How to factor quadratics in () and () format (factored format)
You can use the FOIL Method,
Factoring with 2 perfect squares (the difference of)
You can use the sq root, as the 2 factors (and proceed with your factor formatting)
How do you factor with perfect squares trinomials
Find the sq root - of your 2 square terms (ideally a and b) - those are your factored terms (in factoring format) - then simply square your one factored terms (because the equations itself is already square)
What does the formula for Gradient look like? - this will be in your formula booklet
M=y2-y1/x2-x1
How do you find a parallel line?
If line one and line 2 are parallel then gradient of 1 and gradient of 2 will be the same
How do you tell if lines are perpendicular?
If line one and line 2 are perpendicular, then slope one * slope 2 will equal -1
What are the parameters of the Y = Mx + c equation:
M (gradient) and C (y intercept)-
What is the gradient of a horizontal line?
0
What is the gradient of a vertical line?
Undefined
Equation of a horizontal line:
(0,c), y = c
Equation of a vertical line:
(B,0), is x = b (think of the overall y= Mx + c)
What is gradient intercept form?
Y = mx + c
What is point gradient form? What does it tell you?
Y-y1 = m(x-x1), Parameters are, gradient (M) and point a point(x1, y1)- this will be on the line.
What does general form look like? What are the parameters?
Ax + by + d = 0, used when using integers (integers: not decimals or fractions)
How to use your GDC - finding intersections:
Use y= first, enter your 2 line equations. Then hit graph. From there, you want to hit trace, then 2nd and hit trace again (for calc), and select 5 - or intersect. Then follow the instructions in the calculator- labeling each line before hitting enter angina to guess the intersection.
What do you call a linear function that describes the relationship between 2 variables?
Linear model
What is a linear model see for:
To analyze and predict how the dependent variable will change, in response to to the independent variable (think basic tables and relationship issues) - but know you need to know how to represent these algebraically
What is a quadratic function?
F(x) = ax² + bx + c; a cannot be = to 0
What is the graph of a quadratic function called?
A parabola
What does it mean when a parabola is concave down?
It has a maximum point
When a parabola is concave up?
That means the parabola has a minimum.
What is a vertex?
The max or min point of a quadratic function.
What is the axis of symmetry?
The dashed line through the vertex of a parabola
What is the parent quadratic function (the bare minimum)
Y = x², (0,0) is vertex
What is the ___= for transformations of the parent graph
Y= g(x)
What does a reflection look like:
Y=-x², looks like a reflection over the x axis
What dose a stretch look like:
Vertical stretch is change with scale factor, looks like y=ax² - multiplied by # if that is below 0 its a compression- above its a stretch.
What does a horizontal translation look like
Remember what you expect is opposite, so decimals move left, and full numbers move right. Y = (x -h) ²
What does a vertical translation look like,
This is up and down, y = x² + k, up is #s larger than 0 and down is numbers smaller than 0
Alternate way that translations can be represented:
(HK) on top of each other… H is horizontal and k is vertical. This can represent simple translations.
What does y = -f(x) mean
Reflection across x axis
What does y=f(-x) mean
Reflection across the y axis
Think about how it may be different than vertical dialations- Horizontal dialations:
Y=f(qx)- compared to vertical - variable is insider prentasise
What is vertex form?
F(x)=a(x-h)² + k - a cannot equal 0 - (h,k) are the vertex coordinates- and h is the axis of symmetry
Quadratic equation for General form: What is it
F(x) = ax² + bx =c
Equation for the equation of the axis of symmetry
X= -b/2a
Coordinates of a vertex are:
(-b/2a, f(-b/2a))
Vertex form of a quadratic equation?
F(x) = a(x-h)²+ k
Vertex form - quadratic (X intercepts)
(P,0) (q,0)
Axis of symmetry - intercept form - quadratic
X=p+q/2
What is the intercept quadratic function form?
F(x)=a(x-p)(x-q), a does not = . P and Q are coordinates of the x intercept.
Finding the axis of symmetry - with quadratic factorized form
X= (p+q)/2
Vertex of the quadratic factorized form: - not on formula booklet
(P+q/2, f(p+q/2))
How to switch quadratic general form to a factorized form:
Use your a>1 and 1>a differences - stil the same - just know to add what x= at the end
Finding a quadratic function of a graph:
Start with a(x-p)(x-q) form - factor accordingly
