Solve for x
2sqrt(x)+5=-1
2sqrtx=-6
sqrtx=-3
sqrt(x)^2=(-3)^2
x=9
What 4 transformations occurred in the function
y = -3(x - 2)2 + 4
- translated 2 units to the right
- translated 4 units up
- reflected over the x-axis (upside down)
- Parabola got narrow ( 3 > 1 )
convert to standard form: y = (x + 1)2 - 2
y = (x + 1)( x + 1) - 2
y = (x2 + 2x + 1) - 2
y = x2 + 2x - 1
(3 + 2i) - (3 - i)
0 + 3i
f(x) = x3 + x2 g(x) = x2 - 3
f(2) + g(2)
(x3 + x2) + (x2 - 3)
x3 + 2x2 - 3
(2)3 + 2(2)2 - 3
= 13
(x-5)^2=9
sqrt((x-5)^2)=sqrt9
x - 5 = 3 or -3
x = 8 or 2
write a quadratic equation for the transformations
5 unit up and 3 units left
y = (x + 3)2 + 5
Find the Vertex y = 3x2 + 12x + 5
AOS = (-12)/(2(3))=-2
f(AOS) = 3(-2)^2+12(-2)+5
Vertex = ( -2, -7)
(3 + 2i) (5 - 3i)
15 - 9i + 10i - 6i2
15 + 1i - 6(-1)
15 + i + 6
21 + i
f(x) = x3 + x2 g(x) = x2 - 3
f(x) - g(x)
(x3 + x2) - (x2 - 3)
x3 + 0x2 + 3
= x3 + 3
3x + 4 = 2x - 5
- 2x - 2x
x + 4 = - 5
- 4 - 4
x = - 9
Which is equivalent to y= (x + 2)2 - 2
a. y = x
b. y = x + 2
c. y = x2 + 2
d. y = x2 + 4x + 2
d. y = x2 + 4x + 2
Find the solutions of y = x2 + 2x + 1
x=(-2+-sqrt((2)^2-4(1)(1)))/(2(1))
x = (-2+0)/2
x = -1
(4 + 5i)2
(4 + 5i)(4 + 5i)
16 + 20i + 20i + 25i2
16 + 40i + 25(-1)
16 + 40i - 25
-9 + 40i
f(x) = 4x2 + 2x - 5
Find f(-2)
f(-2) = 4(-2)2 + 2(-2) - 5
f(-2) = 7
find the solution for the equations
y = 4x - 5 and y = -x + 5
4x - 5 = -x + 5
+x +x
5x - 5 = 5
5x = 10
x = 2
Which is equivalent to y = x2 + 3x + 2
a. y = (x + 1)(x + 2)
b. y = (x2 + 3)(x + 2)
c. y = x + (3x + 2)
d. y = (x + 2)2 + 1
Find the solutions of y = x2 - 2x - 8
x=(-2+-sqrt((-2)^2-4(1)(-8)))/(2(1))
x=(2+-6)/2
x= -2 or 4
(2x + 3i)2
(2x + 3i)(2x + 3i)
4x2 + 6xi + 6xi + 9i2
4x2 + 12xi + 9(-1)
4x2 + 12xi - 9
f(x) = 3x3 + 9x2 + 6x and g(x) = 3x2 + 3x
f(x)/g(x)
3x3 +9x2 +6x = 3(x2+3x+2) = 3(x+2)(x+1)
f(x)/g(x)=(3(x+1)(x+2))/(3(x+1)
= (x + 1)
f(x) = (x + 2)(x - 2) and f(x) = 21
(x + 2) (x - 2) = 21
x2 + 2x - 2x - 4 = 21
x2 - 4 = 21
x2 = 25
x = 5 or -5
y = (2x^2+20x+48)/(2x+12)
a. y=(x^2+2x+4)
b. y=x+(20x+4)
c. y=x+4
d. y=x+6
c. y = x + 4
Find the solutions for y = -2x2 + 2x + 4
x = (-2+-sqrt((2)^2-4(-2)(4)))/(2(-2))
x=(-2+-6)/(-4)
x=-1 or 2
(2 - 3i) + (x + 2i)2
(2 - 3i) + (x + 2i)(x + 2i)
(2 - 3i) + (x2 + 4xi + 4i2)
(2 - 3i) + (x2 + 4xi + 4(-1))
(2 - 3i) + (x2 + 4xi - 4)
x2 + 4xi - 3i -2
f(x) = x4 - 4x2 and g(x) = x4 + 14x3 + 24x2
f(x) divide g(x)
f(x)/g(x)=(x^2(x-2)(x+2))/(x^2(x+2)(x+12))
f(x)/g(x)=(x-2)/(x+12)