Forms of Linear Equations
Slope-intercept form of a linear equation:
y = mx + b
Solve:
Seven subtracted from the product of four and a number is 37
4x - 7 = 37
x = 11
Classify the expression:
3x3 + 2x - 1
Cubic Trinomial
Function
What do quadratic functions create when graphed?
A parabola
Standard form of linear equation:
Ax + By = C
Solve using substitution:
y = 2x - 1
2x + 3y = -7
(-1/2, -2)
Simplify:
2x2 - 5x - xy - x3 + 4 - x2 + 3x + 4x3 + 3 + xy
3x3 + x2 - 2x + 7
The name for rate of change of a line.
Slope
Find the axis of symmetry: x = -b/2a
x2 + 12x + 32 = 0
-(12)/2(1) = -6
x = -6
Point-slope form of linear equation:
Hint - this equation form includes an x1 and y1
y - y1 = m(x - x1)
Solve:
3(x - 2) - (x - 6) = 4(x - 7)
x = 14
4x3(x3/x5) - 5xy/y
-x
How do you know if an exponential relationship is increasing?
Hint: b
b>1
Find the vertex, give final answer as (x, y):
3x2 - 6x + 1 = 0
-(-6)/2(3) = 6/6 = 1
3(1)2 - 6(1) + 1 = 0
Final answer: (1, -2)
Use the point-slope equation [y - y1 = m(x - x1)] to find the slope-intercept form of the linear equation.
m = -1
(3, -2)
y - (-2) = -1(x - 3)
y + 2 = -1x + 3
y = -1x + 1
Solve using elimination (addition)
2x + 3y = 20
-2x + y = 4
(1, 6)
(4x2)3(2x)2
64x6(4x2)
256x8
b
Find the discriminant of the quadratic function:
d = b2 - 4ac 9x2 + 6x + 6 = 5
Does the function have 0, 1, or 2 solutions?
d = 0
1 SOLUTION
Translate the slope-intercept equation into standard form:
y = 3/4x - 5
Hint: Ax term can't be negative or fractional
3x - 4y = 20
Solve:
3/4x - 2/3 = 5/6
x = 2
Simplify:
(2x2y)(3x2)/8x6
6x4y/8x6
3y/4x2
f(x) = 2x - 7
find x, when f(x) = -8
-8 = 2x - 7
-1 = 2x
-1/2 = x
Find the zeros of the function by factoring:
5x2 + 17x - 12 = 0
x = {-4, 3/5}