Ch. 1: Equations & Inequalities
(-2)3 + 4(12 - 3)
28
The slope of the line that passes through the points (4, -5) and (-3, 9)
m = -2
How would you draw and shade the graph for this inequality: y > 2x + 1
Dashed line, shaded above the line
What is the line of symmetry for f(x) = x2 + 4x + 5
x = -2
What is the center and radius of this circle: (x-2)2 + (y + 5)2 = 49
Center: (2, -5); r = 7
Solve for x: -3x - 6 = 10
-16/3
The slope of a line perpendicular to a line that goes through the points (3, -1) and (2, -6)
-1/5
Identify where these two lines intersect:
2x + y = 5
3x - y = 5
(2, 1)
What is the vertex of f(x) = x2 + 4x +5
(-2, 1)
Write the standard form of the equation of the circle with radius 3 and center at (1, -4)
(x - 1)2 + (y + 4)2 = 9
Solve: |3x - 2| = 10
x = 4 and x = -8/3
Which relations are functions:
A: (8, 3); (4, 2); (-4, -5)
B: (2, 3); (-2, 1); (2, -5)
C: (6, 3); (-2, 3); (5, 2)
A and C
Simplify: (2sqrt3)(3sqrt15)
18sqrt5
Factor f(x) = x2 + 6x + 5 into intercept form
f(x) = (x + 5)(x + 1)
Complete the square to find the center and radius of x2 + y2 + 6x - 10y - 2
Center: (-3, 5); r = 6
Solve for x: 9 - 2x < 33
x > -12
Write the equation of the line that goes through (-5, 11) and has a slope of 4/5
(y - 11) = 4/5(x + 5) or y = 4/5x 15
Solve: 4x2 + 7 = 32
x = 5/2 & -5/2
What value should be added to both sides to complete the square for x2 - 16x = 3
64
What is the last step to convert this ellipse equation into standard form: 25(x + 2)2 + 8y2 = 200
Divide everything by 200
Solve: |x - 7| < 2
5 < x < 9
Write a direct variation equation if x and y vary directly: x = 10, y = 2
y = 1/5x
Solve: x2 - 4x + 5 = 0
x = 2 + i and x = 2 - i
Write an equation in vertex form for a quadratic with a vertex at (-1, -3) and a point (1, 5)
f(x) = 2(x+1)2 - 3
Convert to standard form: x2 + y2 + 12x + 4y - 9 = 0
(x + 6)2 + (y + 2)2 = 49