unit 2) topic- quadratics Flashcards
(29 cards)
whats standard form
y=ax²+bx+c
whats the vertex
its the highest / lowest point in the middle of the parabola
what is always the axis of symmetry always
its always the x value of vertex
when a is neg what way does parabola open when a is pos what way does it open
a is neg it opens down
a is pos it opens up
whats vertex form
y=a(x-h)²+k
what does h value in vertex form for mean
x-coordinate on the vertex
what does the k value for vertex form mean
y-coordinate on the vertex
how do you write quadratic equation in vertex form
1- find 2 points 1 being the vertex
2- put into equation then add inside the bracket then square it
3- solve algebreicly then rewrite equation with a value included
what do you do when trying to swap factored form/vertex to standard form
1- foil bracket
2- distribuite coeff to bracket
3- add like terms
when a question asks to write a quadratic equation in other words whats it asking
its asking to solve for a then rewrite formula incuding a
how to find x-int on calculator
2nd trace zero then do the left side right side enter
how to find vertex on calculator
2nd trace enter max or minimum moe left right then enter
how to find y-int on calculator
2nd trace value press 0 then enter
whats another way to find the other value of the vertex without calculator
you can just sub the other value into the formula then solve algebraically
what does a question want you to find when it says “zeros” “root solutions”
it means x-int so factored form
what does the equation for factored form look like
y=a(x-r)(x-s)
what do the r and the s stand for in the equation
they stand for 2 x-int
when given 2 points and trying to find vertex/ axis of symmetry wat do you do
you add x values and divide by 2 ( you can only do this when both y values are the same)
how would you solve changing standard to factored form
1- look for gcf
2-factor by looking fro product / sum ect.
3- then make sure to swap signs on the values
(if theres a varible where the x place is make sure to solve algebraicallly)
- remember when theres a coeff and factoring thats what you would divide product sum by if cannot be taken out by gcf
how would you write quadratic equation in factored form when it gives x-int and a point /solving “zeros”
you would do the same you would as if it were a vertex
1- put values into equation
2- add inside brackets / then times 2 terms
3- then solve for a and rewrite a so the value is in equation
how do you find revenue
- R=(price) (#sold)
- (inital price, end price) (inital sold, end sold)
- then graph equation finding vertex
- then using n value which is x on vertex sub into either price () or sold () depending on whats asking
how do you determine quadratic functions
you 1st have to solve for the a value then rewrite in equation switch to standard if it tells you so
when theres a neg in ()^2 for standard form would be neg or pos
it would be pos
whats max revenue
y value on vertex
