Solving Linear, Quadratic, and Exponential Equations

Solving Linear Equations

100

4x + 6 = 26

x = 5

200

-4(x+7) = -20

x = -2

300

3m + 30 = 3(2m +6) 

m = 4

400

5(3x+2) -2 = -2(1-7x)

x = -10

500

A ferry boat carries passengers back and forth between two communities on the Peachville River. It takes 30 minutes longer for the trip upstream. The boat's average speed is 15 mph. The rivers current is usually 5 mph. This equation can be used to find the distance between the two cities.

m/(15-5) = m/(15+5)+0.5

What is the distance between the cities?

10 miles

Solving Quadratic Equations

100

x²=9

± 3

200

-4x²+24=0

±√6

300

-4(x+5)²+5=1

x= -6,-4

400

3x²-8x+10=0

No Solutions

500

Jennifer hit a golf ball from the ground and it followed the projectile h(t)=−16t²+100t, where t is the time in seconds, and h is the height of the ball. 

How long is the golf ball in the air? 

6.25 seconds

Solving Exponential Equations

100

3^x = 9

x=2

200

3^x+10 = 3²⁰

x = 10

300

6^x+2 -3 = 216 

x=1

400

27^x = 9^{x − 2}

x=-4

500

A population of 30 mice is expected to double each year. The number p of mice in the population each year is given by p = 30⁽²ⁿ⁾. In how many years will there be 960 mice in the population?

5 years

Solving Inequalities

100

3x+4 > 16

x > 4

200

4(x+6)-10 > 50

x > 9

300

-2m+6 ≤ 5m -6

x≥2

400

5 > 12a - (3-4a)

x<0.5

500

6x-5(2x+9) ≤ 2x+3

x ≥ -8

Mystery Questions

100

The set of all x values is the....

Domain

200

A function that has a constant rate of change

Linear Function

300

The x-intercepts on a quadratic function can also be called...

Solutions, roots, or zeros

400

The line that an exponential function approaches...

Asymptote

500

 A(n) ___________ function will eventually exceed all others.

Exponential