Factoring
16x2 - 49
(4x - 7)(4x + 7)
Find the equation for the line through the points (-6,4) and (2,1)
y = (-3/8)x + 7/4
or
y - 4 = (-3/8)(x + 6)
or
y - 1 = (-3/8)(x - 2)
Simplify (x2 - 4)/(x2 - x - 2)
(x + 2)/(x + 1)
8(x+4) + 4 = 4x + 1
x = -35/4
Complete the square to find the vertex of x2+5x+4
vertex: (-5/2, -9/4)
x2 + 16x + 60
(x + 6)(x + 10)
Find the equation of the line in slope-intercept form parallel to the line y = 5x - 2 that passes through the point (4,3)
y = 5x - 17
x2/(x-3) + (x-12)/(x-3)
x + 4
-4(-x+2) + 10 = 3 + 10x + 4(x+1)
x = -1/2
Find the vertex of 3x2-12x+9
vertex: (2,-3)
x3 - 2x2 + 5x - 10
(x2 + 5)(x - 2)
Find the equation of the line in point-slope form perpendicular to the line -4x + 2y = 8 that passes through the point (-3,5).
y = (-1/2)x + 13/2
(x+2)/(3x) - (5+x)/(x-2)
(-2x2-15x-4)/(3x2-6x)
or
(-2x2-15x-4)/[(3x)(x-2)]
8 + 3|4x - 7| >= 17
(-infinity, 1] U [5/2, infinity)
Consider the following function: y = -4x2+8x+16
(a) Find its vertex
(b) Does the function have a maximum or a minimum point?
(a) vertex: (1,20)
(b) vertex is a maximum
12x2 - 38x - 14
(3x + 5)(4x - 1)
Find the point(s) of intersection for the two lines with the equations 2x - 4y = 8 and x = 5y + 2
(16/3, 2/3)
[(6x+2)/x + (x-4)/(x+2)]/(x+1)
(7x2+10x+4)/(x3+3x2+2x)
or
(7x2+10x+4)/[(x2+2x)(x+1)]
8 - 3 |4x + 7| = -19
x = 1/2, -4
(a) Find the general equation for the parabola that goes through the vertex (2,1) and passes through the point (3,5)
(b) Is the vertex a maximum or a minimum?
(a) vertex form: y = 4(x-2)2+1 and general form: y = 4x2-16x+17
(b) vertex is maximum
108x2 - 93x - 168
3(9x + 8)(4x - 7)
A pine tree was 27 feet tall in 2004. By 2010, it had grown to 30 feet. If the function which expresses the height of the tree over time is a straight line, how tall will the tree be in 2019?
y = 0.5x + 27 (equation)
answer: 34.5 ft
3/(x-2)
| |2x + 5| - 3 | = 8
x = -8, 3
(a) Find the vertex form of the parabola with vertex (-3/2,-49) passing through point (1/2, -33)
(b) Find its x-intercept(s)
(c) Find its y-intercept
(a) y = 4(x+3/2)2-49
(b) x-ints: (-5,0), (2,0)
(c) y-int: (0,-40)