Quadratics in Standard Form
Factoring (a=1)
Factoring (a>1)
Completing the Square
Graph
100
The standard form of quadratics
y=ax^2+bx+c
100
x^2 -9x +20
(x-5)(x-4)
100
9x^2 -1
(3x +1)(3x-1)
100
What is the first step when completing the square?
Move C
100
What is the vertex ?
(3,-1)
200
The graph of a quadratic function is a ___________.
Parabola
200
x^2 +4x-12
(x+6)(x-2)
200
3x^2+7x+4
(3x+4)(x+1)
200
Completing the square allows us to convert a standard form equation into which form?
Vertex Form
200
T/F Every parabola has at 2 real solutions.
False, a parabola can have 1 solution or 0 solutions
300
Solve
y = x^2 + 2x + 1 at
x=-4
y=9
300
x^2 -13x +22
(x-11)(x-2)
300
4x^2 +5x+1
(4x+1)(x+1)
300
If your b is -10, then what would you need to add to both sides to complete the square?
25
300
How many solutions does this graph have?
No solution
400
The lowest or highest point on a parabola is called the ________.
Vertex
400
x^2 +9x-36
(x+12)(x-3)
400
12x^2 -4x-40
4(3x+5)(x-2)
400
If your b is 40, then what would you need to add to both sides to complete the square?
400
400
Name the zeroes ?
0 and 4
500
The x value of the vertex is also called the...
axis of symmetry
500
x^2 +2x +4
not factorable
500
12x^2 -36x+27
3(2x-3)^2
500
What would you need to add to both sides to complete the square for the quadratic x2 + 8x - 10?
16
500
What are the solutions ?
1 and 3