Factoring / Solving Quadratics
Factor the following: x2-x-20
(x-5)(x+4)
Write the equation of a quadratic in vertex form that has the following transformations:
- Shifted up 2, reflected over the x-axis
y=-x^2 +2
Solve the following quadratic system:
y=x2+3x-5
y=x+3
(-4, -1)
(2, 5)
Factor the following:
x^3-8
(x-2)(x^2+2x+4)
Simplify
sqrt(80)
4sqrt(5)
Factor the following: 28p3-24p2
4p2(7p-6)
Write the equation of a quadratic in vertex form that has the following transformations:
- Translated 3 units right, translated 4 down
y=(x-3)^2 -4
Solve the following quadratic system:
y=x2-4x+6
y=x+2
(4, 6)
(1, 3)
Solve the following:
y=2x^3+8x^2-x-4
x= {-4, sqrt(2)/2, -sqrt(2)/2}
Simplify:
∛54a-6
(3*∛2)/a^2
Factor the following: 7n2+32n-15
(7n-3)(n+5)
Write the equation of a quadratic in vertex form that has the following transformations:
- Vertical stretch by a factor of 6, reflected across the x-axis
y=-6x^2
Solve the following quadratic system:
y=x2+6x-5
y=3x-7
(-2, -13)
(-1, -10)
Factor the following:
x^4 - 16
(x-2)(x+2)(x^2+4)
Simplify:
(sqrt(16a^7))/(∛(8a^3)
2a^2 *sqrt(a
Solve the following quadratic: v2-6v+8=0
v={4, 2}
Write the equation of a quadratic in vertex form that has the following transformations:
- Translated 2 units left
- Shrunk by a factor of 1/2
- Translated 4 units down
y=1/2(x+2)^2 -4
Solve the following quadratic system:
y=x2-8x-20
y=4x+8
(14, 64)
(-2, 0)
Multiply the following:
(2x^2 +5x+2)(2x-1)
4x^3+8x^2 -x-2
Simplify:
∛(2/(3x))
(∛18x^2)/(3x)
x={1/5, 2}
Write the equation of a quadratic in vertex form that has the following transformations:
- Translated 8 units left
- Shrunk by a factor of 1/3
- Translated 3 units up
- Reflection over the x-axis
y=-1/3(x+8)^2 +3
Solve the following quadratic system:
y=x2-10x+14
y=7x-16
(15, 89)
(2, -2)
Divide the following:
(x^3-9x-3)/(x+3)
Hint: You can use long division or synthetic division
x^2 -3x-3/(x+3)
Simplify:
(3+sqrt(5))/(1-sqrt(5)
-2-sqrt(5)