Quadratics in Standard Form
The standard form of quadratics
y=ax^2+bx+c
The vertex form of quadratics
y=a(x-h)^2+k
The factored form of x2+5x+6
(x+2)(x+3)
The process to convert quadratics in standard form to quadratics in vertex form
completing the square
Rewrite into vertex form by completing the square:
x2-4x+8
What is the vertex?
(x-2)2+4
Vertex: (2, 4)
Calculate the x-value of the vertex of
x2-10x+6
h= 5
Vertex of
y = a (x - h)^2 + k
(h, k)
The factored form of
x^2-6x+8
(x-2)(x-4)
The first step in converting a vertex form into standard form (i.e. converting y=(x-4)2+3)
FOIL
Rewrite into vertex form by completing the square:
x2-12x+34
What is the vertex?
(x-6)2+2
(6, 2)
Calculate the x-value of the vertex of:
2x2+8x-3
h= -2
The vertex of
-2 (x - 4)^2 + 2
(4,2)
The factored form of x2-10x+25
(x-5)2
What are a, b, and c of standard form for:
(x+3)2-4
x2+6x+5
a=1
b=6
c=5
Rewrite into vertex form by completing the square:
x2-10x+19
What is the vertex?
(x-5)2+6
(5, 6)
Calculate the x-value of the vertex of:
5x2+15x+67
The Vertex of
y = 2(x-3)^2 - 8
(3, -8)
The factored form of 2x2+5x+3
(2x+3)(x+1)
What are a, b, and c of standard form for:
(x-2)2+2
x2-4x+6
a=1
b=-4
c=6
Rewrite into vertex form by completing the square:
2x2-8x+8
What is the vertex?
2(x-4)2
(4, 0)
Calculate the x value of the vertex:
-2t2-12t+15
h=-3
Vertex of
-4 (x + 6)2 - 4
(-6, -4)
The form of a perfect square trinomial
x2+bx+(b/2)2
What are a, b, and c of standard form for:
(x+7)2-40
x2+14x+9
a=1
b=14
c=9
Rewrite into vertex form by completing the square:
3x2-18x+40
What is the vertex?
3(x-3)2+13
(3, 13)