Quadratics Flashcards
What is an algebraic expression?
consists of products of numbers and letters1
What is a coefficient?
the initial number multiplying the letter afterwards
What is a polynomial?
1 unknown in algebraic expression
What is a function input?
x
What is a function output?
f(x)=
What is D.O.T.S?
Difference of two squares
What is an equation?
Has 1 letter in it with an equals that should be solvable
What are the inequalities?
> < _< _>
What is a linear equation?
a straight line in form y=mx+c
What is an identity?
When something equals on each side left=right
What are facts about a quadratic graph?
- 2 points intersect x axis = through
- 1 point of intersection of x axis = bounces
- no roots = floats above x axis
How do you find x and y root intercepts?
to find x intercepts y=0
to find y intercepts x=0
How do you find the minimum/maximum points on a graph?
complete the square
x coordinate makes inside bracket 0
y coordinate is outside the bracket on the right
What is a negative graph of x^2 look like?
when the coefficient of x^2 is negative
opposite for positive graph
How do you rearrange the quadratic equation to the quadratic formula?
ax^2+bx+c=0 - take out a a(x^2+bx/4)+c=0 - complete square a((x+b/2a)^2/b^2/4a^2)+c=0 - multiply by a a(x+b/2a)^2-ab^2/4a^2 +c=0 - cancel a out a(x+b/2a)^2 = b^2/4a -c=0 - divide by a (x+b/2a)^2 = b^2/4a^2 -c/a - multiply by 4a (x+b/2a)^2 = b^2-4ac)/4a^2 - square root x+b/2a = sqr(b^2-4ac/4a^2) - minus by b/2a x = -b/2a +/- sqr(b^2/4ac/2a) - all over 2 a (collect like terms) x = (-b+/- sqr(b^2-4ac)/2a)
