Chapter 1 Review (Pre-Calc)

Linear Equations

100

Write an equation of the line passing through the points (0,0) and (3,6).

y = 2x

200

Write an equation of the line with slope 1/2 passing through the point (7, 2).

y = 1/2 (x - 7) + 2

300

Write an equation of a horizontal line with y-intercept 2.

y = 2

400

Write an equation of a vertical line with x-intercept -6.

x = -6

500

A line passes through (-1,2) and (2,-4).

Write the equation of the line in point slope form, slope intercept form, and standard form.

y = -2(x - 2) - 4

y = -2x

2x + y = 0

Linear Functions

100

Identify the domain and range of the linear function
y = -2x + 4/3

all real numbers

200

Identify the slope and y intercept of the function
f(x) = -1/3 x + 6

m: -1/3; intercept: 6

300

Identify the x and y intercepts of the function
f(x) = -2x + 4

y-int: (0,4)
x-int: (2,0)

400

Identify the domain and the range of the linear function: y = 4

domain: all real numbers
range: 4

500

Explain why the linear equation below does not represent a function.
x = 6

All values in the range have a corresponding domain value of 6. 

Doesn't pass the vertical line test... because it is a vertical line.

Quadratic Equations

100

Solve the quadratic equation:

3x^2+6x+3=0

x = -1

200

Solve the quadratic equation:

x^2-7x-18=0

x=9, -2

300

Solve the quadratic equation:

4x^2+3x-10=0

x=-2, 5/4

400

Solve the quadratic equation:

6 x^2 - 7 x - 5 = 0

x= 11/2, x= 5/3

500

Solve the quadratic equation:

2x^2+3x+10=0

x = -3/4 +- (i sqrt(71))/4

Quadratic Functions

100

Describe the vertex, direction, and shape of the quadratic function:

y=(x-1)^2+3

vertex: (1,3)
direction: opens upward
shape: over 1 up 1, "normal"

200

Describe the vertex, direction, and shape of the quadratic function:

y=-2(x+2)^2

vertex: (-2,0)
direction: opens downward
shape: over 1 down 2, "narrow"

300

Describe the vertex, direction, and shape of the quadratic function:

y=4x^2+4x+1

vertex:(-1/2, 0)
direction: opens up
shape: over 1 up 4, "narrow"

400

State the vertex and ALL intercepts of the quadratic function:

f(x)=(x-2)^2-4

vertex: (2,-4)
x-intercepts: (0,0), (4,0)
y-intercepts: (0,0)

500

State the vertex and ALL intercepts of the quadratic function:

f(x)=(x-3)^2-4

vertex: (3,-4)
x-intercepts: (1,0), (5,0)
y-intercepts: (0,5)

Complex Numbers

100

Simplify (remove the negative root).

sqrt(-32)

4isqrt(2)

200

Add.

sqrt(-50)+sqrt(-8)

7isqrt(2)

300

Multiply: 

(3+i)(3-i)

10

400

Multiply:

(3+2i)(2-3i)

12-5i

500

Write in the form a + bi.

2/(3+i)

(3-i)/5