Formulas
What is the formula for h
h=-(b)/2a
x^2+2x+1=0
x=-1
3x+36
3(x+12)
y=x^2
y=(x-5)^2
Shift to the right 5
What is the domain and range
Domain: x-values
Range: y-values
What is the vertex form formula
y=a(x-h)^2+k
x^2+6x-10=30
x=4 x=-10
4x^2+16x
4x(x+4)
y=x^2
y=(x+8)^2-13
Shift to the left 8 and go down 13
What is the radicand?
The number under the radical symbol
What is the formula for k
k= 4ac-b^2/4a
8x^2=15-14x
x=3/4 x=-5/2
x^2-14x-40
(x-10)(x-4)
y=x^2
y=1/2(x-8)^2+13
Vertically compress by a factor of 1/2, shift 8 to the right, and go up 13 units
What does it mean to rationalize?
To eliminate a radical or an imaginary number from the denominator of an algebraic expression
What is the standard form formula
y=ax^2+bx+c
4x^2+2x=12
x=-2 x=3/2
-8x^2-15x+2
(-8x+1)(x+2)
y=x^2
y=3(5x+17)^2-9
Verticle stretch by a factor of 3, compress the graph by a factor of 5, shift 17 to the left, shift down 9
What is an extraneous solution?
An apparent solution that must be rejected because it does not satisfy the original equation.
6x^2-48x-54=0
x=9 x=-1
4x^2+17x-15
(4x-3)(x+5)
y=x^2
y=1/3-(7x+7)^2-9
Compress the graph vertically by a factor of 1/3, compress the graph horizontally by a factor of 7, reflect over the y-axis, shift 7 to the left, and go down 9
What is Direct Variation?
Relationship of variables x and y whereas one quantity increases/decreases the other quantity increases/decreases/