# GRAPHING FORMULAS

```GRAPHING FORMULAS
Slope intercept
y  mx  b
↓
Slope
↓
y-intercept
Point – Slope
y  y1  m( x  x1 )
Slope-Formula
m
y 2  y1
x 2  x1
How to label points: ( x1 , y1 )( x2 , y2 )
Standard Form of a Linear Equation ax  by  c
c
b
y-intercept =
Slope 
a
b
Standard Form of a Quadratic Equation
ax 2  bx  c  0
Vertex Form of a Quadratic Function
f ( x )  a ( x  h) 2  k
where (h, k) is the vertex
 b  b 2  4ac
x
2a
x
Vertex Formula
Discriminant
Vertical Lines
Horizontal Lines
Parallel Lines
Perpendicular Lines
y  x
2
y  x
 2x  1
2
 2x 1
Circle Formula
b
2a
b 2  4ac
Use the discriminant to determine the number & type of solutions to a quadratic equation.
Positive = Two real solutions /Zero = One real solution / Negative = two complex, but not real solutions
xN
yN
(Slope is undefined)
(Slope = 0 )
Slopes are identical
Slopes are negative reciprocals. (when you multiply the two slopes you get -1)
a parabola that must go down because the Coefficient –x2 value is negative.
a parabola that must go up because the x2 value is positive
( x  h) 2  ( y  k ) 2  r 2
Where (h, k) is the center and (x, y) is any point on the circle
Midpoint Formula
 x1  x 2   y1  y 2 
 , 


 2   2 
Distance Formula
d   x 2  x1  2  ( y 2  y 1 ) 2
Factoring: Cube Formulas
(a  b)(a 2  ab  b 2 ) and (a  b)(a 2  ab  b 2 )
Saved: Math HANDOUT (Graphing Formulas) {Tutorial Support Services Mission del Paso Campus } sources: Textbook Algebra a Combined Approach by Elayn Martin-Gay (black cover)
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