Quadratic Equations and Functions/ factoring Vocabulary

17 terms by 14APARK 

Create a new folder

Advertisement Upgrade to remove ads

Quadratics

expressions of the form ax2+bx2+c

Quadratic Equations

form ax2+bx2+c=0 where "a" does not equal to zero. May have two, one, or zero solutions.

Linear Equations

equations of the form ax+b=0 where "a" does not equal 0 and only have one solution.

x2=k

x= positive or negative square root of k (k>0)
x= 0 (k=0)
there are no real solutions (k<0)

Null Factor Law

when the product of two or more numbers is zero, then at least one of them must be zero. If ab=0 then a=0 or b=0.

Null Factor Law Steps

1. If necessary, rearrange the equation so one side is zero.
2. Fully factorise the other side (usually LHS)
3. Use the Null Factor Law
4. SOlve the resulting linear equations
5. Check at least one of your solutions

Ilegal Cancelling

We must never cancel a variable that is a common factor from both sides of an equation unless we know that the factor cannot be zero.

Quadratic Formula

If ax2+bx+c=0 where "a" does not equal to zero, then x = -b ± √(b² - 4ac)/2a

Quadratic Function

relationship between two variables which can be written in the form y=ax+bx+c where "x" and "y" are the variables and a, b, and c are constants, "a" does not equal to zero. (using function notation, can be written as f(x) = ax2+b+c

Conic Sections

curves which can be obtained by cutting a cone with a plane. Ancient Greek mathematicians were fascinated by conic sections

Parabola

name comes from the Greek word for "thrown" because when an object is thrown, its path makes a parabolic arc. Examples are parabolic mirrors used in car headlights, heaters, radar discs, etc.

Simplest Quadratic Function

y = x2
- curve is a parabola and opens upwards
- no neg. y values, curve doesnt go below the x-axis
- curve is symmetrical about y-axis
- curve has turing point or vertex at (0,0)

x-intercept

value of "x" where graph meets the x-axis and are found by letting "y" be 0 in the equation of the curve ( easy to find when quadratic is in factorised form)

y-intercept

value of y where the graph meets y-axis and are found by letting "x" be 0 in the equation of the curve (constant term in quadratic function)

factorising to find x-intercepts

any quadratic function, the x-intercepts can be found by solving the equation ax2+bx+c=0.

Graph of any quadratic function

- is a parabola
- has turning point or vertex
- is symmetrical about a line of symmetry

line of symmetry

equation of y=ax2+bx+c is x=-b/2a

Please allow access to your computer’s microphone to use Voice Recording.

Having trouble? Click here for help.

We can’t access your microphone!

Click the icon above to update your browser permissions above and try again

Example:

Reload the page to try again!

Reload

Press Cmd-0 to reset your zoom

Press Ctrl-0 to reset your zoom

It looks like your browser might be zoomed in or out. Your browser needs to be zoomed to a normal size to record audio.

Please upgrade Flash or install Chrome
to use Voice Recording.

For more help, see our troubleshooting page.

Your microphone is muted

For help fixing this issue, see this FAQ.

Star this term

You can study starred terms together

NEW! Voice Recording

Create Set