Linear and Quadratic Functions
Recall: If a line passes through (x1 , y1 ) and
(x2 , y2 ) , its slope m is given by
The sign of the slope indicates whether the line is an
increasing or a decreasing function.
m < 0
m > 0
1. The slope of any horizontal line is 0.
2. The slope of any vertical line is undefined.
Two lines are parallel if they never cross. In terms of equations, two lines are parallel if
they have __the same_____ slope.
Two lines are perpendicular if they meet at a right angle. In terms of equations, two lines
with slopes m1 and m2 are perpendicular if and only if
m1* m2 = -1 .
Example 2: Find the linear function f such that f
(1) = 5 and f (2) = 8 . What is the inverse of this
Example 3:Write the equation of the linear function
f(x) that passes through the point (-4,5)
and is parallel to the line 4x + 3y = 7 .
Example 4: Find the linear function f that is
perpendicular to the line containing (4,-2) and
(10,4) and passes through the midpoint of the line segment connecting these points.
Every quadratic function also know as a parabola is
written as f (x) = ax2 + bx + c or can be written in
standard form: f (x) = a(x - h)2 + k . The vertex is (h, k) . The y-intercept is f(0). The axis of symmetry is
the equation x = h.
You should be able to identify the following :
· Direction the graphs opens(upwards or downwards)
· Whether the function has a maximum or a minimum
· coordinates of the vertex
· equations of the axis of symmetry
· maximum or minimum
Example 5: Sketch the graph of f (x) = 3x2 + 6x + 7 by finding the six features of the function.
Example 6: Sketch the graph of f (x) = -2x2 + 12x - 16 by finding the six features of the function.
Example 7: Find the quadratic function such that
the axis of symmetry is x = - 2 , the y-intercept is - 6
and there is only one x-intercept.