Completing the Square
Solve for p by completing the square: p² + 14 p − 38 = 0
p = -7 + (√87), -7 - √87
What is the quadratic formula?
x = (-b +- √b2 - 4ac)/2a
Team: Find the discriminant and analyze the roots: 2x2 - 7x = 5 x = (7 +- √85) / 4
Discriminant = 89
Roots = 2 real, irrational roots
If I were to solve the following Quadratic, what would n be? (5x-3)² - 4(5x-3) - 19 = 0
Answer: (5x-3)
The following graph moves ___ : f(x)=(x² -9)
9 units down
Solve for a by completing the square: a² +14a - 51 = 0
a = -17, 3
Team: Solve using the quadratic formula: 8x2 = 15 - 14x
x = ¾, -5/2
Team: Find the discriminant and analyze the root: 3x2 = 10x + 4
Discriminant = 148 Roots: 2 real, irrational roots
Find the n term in the following quadratic: x-4 - 6x-2 + 13 = 0
n = x-2
also written as: 1/(x2)
Name the vertex of the parabola: f(x)=(x+4)²
-4,0
Solve for x by completing the square: x² + 6x + 8 = 0
x = -4, -2
Team: Solve using the quadratic formula: x2 + 6x = 14
x = -3 +- (√23)
Team: Find the discriminant and analyze the root: 4x2 - 6x = 14
Discriminant = 260 Roots: 2 real, irrational roots
Solve for x: (x-1)² + 7(x-1) + 12 = 0
x = -2, -3
Name the vertex of following parabola and is it a max or min: f(x)=-(x+7)²
vertex of (-7,0), max
Solve for x by competing the square: x² + 14x - 15 = 0
x = -15, 1
Team: solve using the quadratic formula: -5x2 + 3x = 11
x = 3/10 +- (i√211) / 10
Team: Find the discriminant and analyze the root: 4x2 + 5 = -6x
Discriminant = -44 Roots: 2 imaginary roots
Solve for y: y⁴ + 3y² - 28 = 0
y = -2, 2
Rewrite the following in h,k format: y = 3x²-6x+5
y = 3(x-1)²+2
Solve for r by competing the square: r² - 4r - 91 = 7
r = 2 + (√102), 2 - (√102)
Team: solve using the quadratic formula: 1/6x2 + 4/3x - ⅔ = 0
x = -4 +- 2√5
Team: Find the discriminant and analyze the root: 3x + 7 = -5x2 - 4
Discriminant = -211 Roots: 2 imaginary roots
Solve for x: x + 16√x - 36 = 0
x = 4
Rewrite in h,k form, name the vertex, is it a max or min: y=x²+12x+32
y=(x+6)² - 4, (-6,-4), min