Graphs
The vertex of y = -3(x + 2)2 - 8
(-2, -8)
Tells us the x-coordinate of the vertex and also the axis of symmetry
x = -b/2a
When solving using square roots, this always goes in front of the radical
plus or minus sign
The vertical line that passes through a parabola's vertex
Axis of Symmetry
Factor 4x2 - 49
(2x + 7)(2x - 7)
The axis of symmetry of y = 2x2 + 8x + 3
x = -2
First step in converting y = 4(x + 6)2 - 3 to standard form
Expand (or FOIL) (x + 6)2
The max height of y = -1/12(x - 255)2 + 312
312
y = a(x - h)2 + k
Vertex Form
simplified form of (1 + 2i)(3 - 4i)
11 + 2i
The vertex of y = 3x2 + 9
(0, 9)
First step in converting y = 3x2 + 6x - 5 to vertex form
Use x = -b/2a and find the vertex
Solve by factoring: x2 + 9x + 8 = 0
x = -1, -8
y = ax2 + bx + c
Standard Form
Vertex
The transformations to get y = x2 to y = -3(x + 4)2
The Quadratic Formula
x = [-b +-sqrt(b2 - 4ac)]/(2a)
Solve using square roots: -3x2 - 3 = 45
4i, -4i
Tells us how many solutions a quadratic equation has
Discriminant OR b2 - 4ac
Factor completely: 3x2 + 12x + 12
3(x + 2)(x + 2) OR 3(x + 2)2
Point on a parabola that represents "where an object hits the ground"
x-intercept
In a word problem, to find out the "starting height" of the object
The cost of producing x units is given by C = 0.04x2 - 8.504x + 25302. Find the number of units that will minimize the cost, and find the minimum cost.
106.3 units, $24,850.01
Another name for the vertex of a parabola if the parabola opens down
Maximum
The number of solutions of 2x2 + 4x + 3 = 0
Zero