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What does the Nonlinear Functions revision sheet cover?

Nonlinear means the rate of change itself changes, One quadratic, three forms, standard form, and c is the y-intercept, vertex form, vertex at (h,k), factored form, x-intercepts at p and q, axis of symmetry, which is also the x of the vertex, sum of the two roots, with no factorising at all, Worked: intercepts and vertex, Which way the parabola opens, a is positive, a is negative, Exponential models.

Is this for Digital SAT SAT Math?

Yes, it is written for the Digital SAT SAT Math syllabus.

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Nonlinear Functions — Digital SAT SAT Math revision notes

A 3-page visual revision sheet for Nonlinear Functions, written for Digital SAT SAT Math. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.

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Nonlinear Functions in one look

parabolas, exponentials, and what a shift does to an equation

Nonlinear means the rate of change itself changes

a linear function adds the same amount every step. A quadratic adds a growing amount, and an exponential multiplies by the same factor every step
that one distinction answers most of the modelling questions: added each time is linear, multiplied each time is exponential
a quadratic drawn on axes is a parabola, and every parabola has a vertex (its highest or lowest point) and an axis of symmetry through it
the graph of a function and its equation carry the same information. The question decides which of the two is quicker to read

One quadratic, three forms

standard form, and c is the y-intercept y=ax^2+bx+c
vertex form, vertex at (h,k) y=a(x-h)^2+k
factored form, x-intercepts at p and q y=a(x-p)(x-q)
axis of symmetry, which is also the x of the vertex x=-b/2a
sum of the two roots, with no factorising at all p+q=-b/a

Worked: intercepts and vertex

Q. h(x)=x^2-8x+12. What is the sum of the x-intercepts of y=h(x), and where is the vertex?

x-intercepts are the x values with h(x)=0: x^2-8x+12=0
factorise: (x-2)(x-6)=0, so x=2 and x=6
their sum is 8, which is also -b/a=8, so the factorising was optional for this part
the vertex sits on the axis of symmetry, midway between the roots: x=2+6/2=4
substitute back for the height: h(4)=16-32+12=-4

Answer: the intercepts sum to 8, and the vertex is (4,-4)

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What this Nonlinear Functions sheet covers

Nonlinear means the rate of change itself changes
One quadratic, three forms
standard form, and c is the y-intercept
vertex form, vertex at (h,k)
factored form, x-intercepts at p and q
axis of symmetry, which is also the x of the vertex
sum of the two roots, with no factorising at all
Worked: intercepts and vertex
Which way the parabola opens
a is positive
a is negative
Exponential models
the general shape, b multiplied on each step
a rise of r per period, r as a decimal
a fall of r per period
Worked: writing an exponential model
Transformations: inside against outside
Which form does this question want
Pacing and the graphing calculator
Symbols and terms
Traps that cost points
Tricks that save time

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