Solving linear equations and inequalities: foundations

Write a template linear equation with no solutions for values of x

a = b

Write a template linear equation with an infinite number of solutions for values of x

x = x

When do two lines intersect once

When they have different slopes.

When do two lines completely overlap

When they have the same y-intercept and slope

When do two lines never intersect

When they have the same slope but different y-intercepts.

Explain the sketch of a linear inequality graph

• <= and => inequalities show a solid line on the graph

• < and > inequalities show a dashed line on the graph

• solutions to the function are shaded

State the formula for exponential growth/decay

The formula for exponential growth is given by y = a(1 ∓ r)^t, where a is the initial amount, r is the growth rate, and t is time.

Complete the square of a template quadratic expression

• x² - 2x +1

• (x - 1)² + 1 - 1

• (x - 1)²

Shift a function c units to the right

f(x - c)

Shift a function c units to the left

f(x + c)

Shift a function c units up

f(x) + c

Shift a function c units down

f(x) - c

Reflext a function across the x-axis

-f(x)

Reflext a function across the y-axis

f(-x)

Stretch a function vertically

c f(x)

Stretch a function horizontally

f(xc)

State the polynomial remainder theorem

for a function f(x) divided by x - a, the remainer = p(a)

State Pygotharas’ theorem

For a right angled triangle, a² + b² = c² where c is the hypotenuse

State the isosceles circle theorem

a triangle that contains two radii is an isosceles triangle

Write the standard form of a circle equation

(x - x₁)² + (y - y₁ )² = r²

• x₁ , y₁ = center of circle

• _{r = radius}