8.1 - completing the square
What are the steps to completing the square
Move the c term to the other side
Divide both sides by a
Half b and square it
Add (1/2 b)2 to both sides
Factor the left side
Square root both sides
Solve for x
State the Quadratic Formula
x= (-b +- sqrt (b2 - 4ac)) / (2a)
What is the discriminant? and What does it tell us?
b2 - 4ac. It tells us how many and what kind of roots a quadratic function has.
What is the standard form of a Parabola?
f(x) = ax2 + bx + c
where the vertex is (-b/2a, f(-b/2a))
What is the Vertex form of a parabola?
f(x) = a(x - h)2 + k
where (h, k) is the vertex
Fill in the blanks for the perfect square trinomial:
x2 + 7x + ___ = (x + ___)2
49/4 : 7/2
Solve using the quadratic formula:
x2 - 4x +1 = 0
x = 2 +- sqrt(3)
Find the discriminant and analyze the roots:
3x2 +5x +6 = 0
-47: 2 imaginary roots
solve for x:
(3x-2)2 - 5(3x-2) - 6 = 0
x = 1/3, 8/3
Describe the transformation from x2 and the sketch of the graph (vertex, open up or down)
f(x) = -(x+4)2 - 9
Left 4, Down 9, vertex at (-4, -9), Upside-down
Solve by completing the square:
x2 - 18x + 81 = 1
x = 8, 10
Solve using the quadratic formula:
2x2 - 4x + 5 = 6x -7
x = 2, 3
Find the discriminant and analyze the roots:
4x2 + 28x + 49 = 0
0: 1 real, rational root
Solve for x:
6(4x - 5)2 +13(4x - 5) +6 = 0
x = 7/8, 13/12
Write an equation for the transformation from the parent function x2
Down 3
f(x) = x2 -3
Solve by completing the square:
3x2 - 12x - 4 = 0
x = (6 +- 4 sqrt(3)) / 3
Solve using the quadratic formula:
9x2 - 6x +1 = 0
x = 1/3
Solve using any method:
2x2 - 4x + 5 = 0
x = (2 +- i sqrt(6)) / 2
Solve for x:
8(1/3x)2 + (10/3x) - 3 = 0
x = -2/9, 4/3
Given the vertex (-2, -1) and point (-1, -6) on the parabola, find an equation in f(x) = a(x-h)2 + k form.
f(x) = -5(x+2)2 - 1
Solve by completing the square:
x2 - 4x +16 = 0
x = 2 +- 2i sqrt(3)
Solve using the quadratic formula:
3x2 +9x = 5(x-1)
x = (-2 +- i sqrt(11)) / 3
Solve using any method:
5x2 - 15 = 21
x = +- 6 sqrt(5) / 5
Solve for x:
3x-4 + 11x-2 - 4 = 0
x = +- sqrt(3)
Rewrite 3x2 +12x -8 in vertex form
Name the vertex
Is the vertex a max or min?
f(x) = 3(x+2)2 - 20
(-2, -20)
minimum