How to use a graph to solve a system
The intersecting points are the solutions
If the two don’t intersect…
No solution
How to solve with graphing
Graph both and find where they intersect
How to graph a line
Y = mx+b
Plot (0,b)
Use m to count rise and run
How to graph a parabola
Find a, b, and c
Find x by using -b/2a
Plug x into the original equation to find y
Plot vertex: (x,y)
Use (0,c) for an additional pt.
How to solve a system using substitution
Insert the y= or x= into the other equation (or make it so that y= something)
Make it into a quadratic ax²+bx+c=0 and solve like normal to get x (and sometimes -x)
Plug the x(s) into the original equation to get y(s)
How to solve a system using elimination
Remove one variable by adding the two equations
Solve for the variable
Plug into the original equation to get the other variable
How to graph parabolas as inequalities
- Determine whether the lines are dotted/solid
- Graph like an equation
- Pick a point inside the parabola to plug in.
True- shade inside False- shade outside
How to graph a system
Do both
parabola, parabola
parabola, line
Shade overlapping
How to solve algebraically
- Find the zeros by solving the equation
- Place both on the line
- Pick 2 #’s, one between -infinity and the 1st # and one between the 1st and 2nd #
- Plug both #’s into the equation and see which one is true
- Write the equation
How to write the equation of an algebraic # line
If it ≤ ≥ use [ ] but only on the side with the #’s
If it < > use ( ) on both sides
On the left, use negative infinity, and on the right, use infinity
Are you done after finding x in an inequality?
No, you have to plug x into the original equation to find y.
How to put a quadratic into vertex form
- Divide bx by 2 and square it
- Add that number to ax² +bx and subtract it from c but keep them separate
- Write the ax²+bx+# as a perfect square
- Subtract c-#
- Write vertex.
