Characteristics of Quadratics
Find the vertex:
y = x2 +6x + 2
(-3, -7)
Graph:
y = x2 + 4x + 6
vertex: (-2, 2)
opens up
over 1, up 1
over 1, up 3
over 1, up 5
Solve by factoring:
x2 - 4x - 32 = 0
x = 8, -4
Solve using square roots:
3x2 = 48
x = 4, -4
How many solutions does the equation have?
x2 + 2x + 1 = 0
1 real solution
Find the axis of symmetry:
y = 3x2 + 12x - 12
x = -2
Graph
y = 2x2 - 6
vertex: (0, -6)
opens up
over 1, up 2
over 1, up 6
over 1, up 10
Solve by factoring:
x2 - 8x + 15 = 0
x = 3, 5
Solve using square roots:
36x2 - 49 = 0
x = 7/6, -7/6
Solve using the quadratic formula:
3x2 + 1 = 2x
no real solutions
Find the axis of symmetry.
y = -2x2 + 4x
x = 1
Graph:
y = -x2 + 2x + 3
vertex: (1, 4)
opens down
over 1, down 1
over 1, down 3
over 1, down 5
Solve by factoring:
2x2 - 5x - 3 = 0
x = -1/2, 3
Solve using square roots:
(x + 2)2 = 9
x = 1, -5
How many solutions does the equation have?
x2 + 4x - 5 = 0
2 real solutions
Find the vertex.
y = 3 + 4x - 2x2
(1, 5)
Graph:
y = -2x2 + 4x - 3
vertex: (1, -1)
opens down
over 1, down 2
over 1, down 6
over 1, down 10
Solve by factoring:
x2 + x = 6
x = 2, -3
Solve using square roots:
(x - 4)2 = -4
no real solution
Solve using the quadratic formula:
x2 - 6x - 7 = 0
x = -1, 7
Does the graph open up or down?
y = -3x2 + 7x +12
Graph:
y = x2 + 4x - 3
vertex: (-2, -7)
opens up
over 1, up 1
over 1, up 3
over 1, up 5
Solve by factoring:
-8x - 33 = -x2
x = 11, -3
Solve using square roots:
(x - 5)2 = 25
x = 10, 0
Solve using the quadratic formula:
3x2 - 2x = 8
x = -4/3, 2