DE College Algebra & Elementary Calculus '25-26

Keepin’ It Imaginary

100

SOLVE: i³

−i

200

−√−81

−9i

300

(8 + 2i) − (7 − 4i)

1+6i

400

(13+2i)(11−4i)

151−30i

500

 7−2i/3+4i

13/25 + 34/25i

Root Awakening ☕

100

Find the roots: x² = 36

x=±6

200

Factor by completing the square: 

x²+ 5x − 14 = 0

x=−7,2

300

2x²−5x−12=0

x=4, -3/2

400

Solve. 

f(x)=x²−4x−24

x= 2±2√7

500

3x²−10x+14=0

5/3 ± √17/3i

Function Junction 🚂

100

Find the vertex: f(x)=x²+4x−1 

(−2,−5)

200

Find the vertex, AOS, & domain/ranges: f(x)=x²−4x+3

Vertex: (2,−1)

AOS: x=2

Domain: (−∞,∞)

Range: [−1,∞)

300

Find vertex, AOS, inc/dec, and dom/range: f(x)=−2x²+8x−3

vertex: (2,5)

AOS: x=2

inc/dec: (−∞,2) to (2,∞)

dom/range: (−∞,∞) , (−∞,5]

400

Find the vertex, AOS, max/min, dom/range, and inc/dec for the function: f(x)=−3(x−2)²+5

• Vertex: (2,5)

• Axis: x=2

• Maximum: 5

• Domain: (−∞,∞)

• Range: (−∞,5]

• Increasing: (−∞,2)

•  Decreasing: (2,∞)

500

A quadratic function G(x) has a vertex at (4,−2) and passes through the point (−1,53). Determine the final equation in vertex form. 

G(x)=11/5 (x−4)²−2

Rational Rebels💥

100

solve the radical: √6x+1=4 

x=5/2

200

Solve for x: 

x+3/ x-2= 4/ (x+1) - 4/ x²-x-2

x=±i√ 15

300

Solve for x.

(x+4)/4 −(2x−7)/3 = 0

x=8

400

Solve for x.

1/x − 1/ x+1 +1/ x+2 = 0

x=-1±i

500

Solve. 

(x-2)/(x+4) =6 / (x-1) - 6 / x²+3x-4

x= 9 ± √ 145 / 2 

Absolute Madness

100

Solve the following.

|2x+1|-6=19

x=12, −13

200

In absolute value inequalities, this word describes the solution where a number must satisfy both conditions at the same time. 

What is AND? 

300

|2x−5|<7

−1<x<6

400

5−3|4x−7|=−10

x=3 OR x=1/2

500

2−3|5x−4|=−7

x=1/5 OR x=7/5