Forms of Quadratics
What is the parent function for a quadratic?
y=x2
Use Box Method or FOIL to solve:
(x+2)2
y=x2+4x+4
In standard form, what letter represents the y-intercept?
C
What can we identify when we have an equation in factored form?
Roots, zeroes, solutions.
When we rewrite these terms, into standard form, which term will come first?
2x+17-4x3+18x4+1
18x4
The x-intercepts are also called the roots. What are the other two names for the x-intercepts?
Zeroes and Solutions
Use Box Method or FOIL to solve:
(x+5)(x+4)
x2+9x+20
Which form would you use in order to find the vertex?
Vertex Form
Convert to general form:
y=(x+5)(x+4)
y=x2+9x+20
What is the y-intercept of this equation?
y=12x2-15x+1038
1038
What form is this equation in?
y=0.5(x+8)2-7
Vertex Form
Use Box Method or FOIL to solve:
(-2x-2)(5x2-6x+5)
-10x3+2x2+2x-10
Identify the roots from this equation:
y=5(4x+8)(x+7)
r1=-2 r2=-7
Convert to general form:
y=2(x-5)(x-1)
y=2x2-12x+10
Convert to Standard Form and find the y-intercept:
y=3(x+7)2
y=3x2+42x+147
(0, 147)
Write the equation for Factored Form
y=a(x-r1)(x-r2)
Use Box Method or FOIL to solve:
(-2x-5)(-2x2-x-6)
4x3+12x2+17x+30
y=-2(x+4)(x-2)
(0, 16)
Determine the y-intercept of:
y=0.5(x+2)(x+5)
(0, 5)
Convert the equation to standard form and find the y-intercept:
y=-5(x-4)2-3
y=-5x2+40x-83
(0, -83)
Where on our graph do we find the roots?
Use Box Method or FOIL to solve:
(-6x2+3x+3x3+6)(x-5)
3x4-21x3+33x2-9x-30
Use the equation to find the vertex and the line of symmetry:
y=5(x+3)(x+5)
Vertex: (-4, -5)
L.O.S. is at x=-4
Determine the vertex and the line of symmetry from the following:
y=5(x-1)(x+5)
Vertex: (-2, -45)
L.O.S. is at x = -2
Determine the vertex and y-intercept of this equation:
y=2(x-6)2-6
Vertex: (6, -6)
Y-Int: (0, 66)