Page 567 - Algebra 1

The direction of a parabola can be determined by value of the coefficient of the quadratic term.
Determining the Direction of a Parabola
Determine whether the graph of each function opens upward or downward.
a. f(x)=3x2 +8
SOLUTION
f(x)=3x2 +8 a=3
The graph opens upward because a > 0.
b. f(x)=3x-x2 +5
SOLUTION
f(x)=3x-x2 +5
f(x) = -x2 + 3x + 5 Write in standard form. Since a = -1, a < 0 and the graph opens downward.
Application: Free Fall
A pebble is dropped from a 256-foot-tall cliff. The equation 256 - h = 16t2 can be used to find the height h of the pebble after falling for t seconds. Find the height of the pebble after falling for 2 seconds.
SOLUTION
Understand Determine the height of the pebble using the function 256 - h = 16t2. Define the variables in the function.
h = height in feet t = time in seconds
Plan Solvetheequationforheighth,andthenfindhwhent=2. Solve Solvetheequationforheighth.
256 - h = 16t2 h=-16t2 +256
Find h when t = 2. h = -16t2 + 256
= -16(2)2 + 256
= 192 feet
The height of the pebble after falling for 2 seconds is 192 feet.
Direction of a Parabola
For a quadratic function in standard form, y = ax2 + bx + c: If a < 0, the parabola opens downward.
If a > 0, the parabola opens upward.
Example
3
Example
4
Math Reasoning
Analyze If a pebble were dropped from a 144-foot-tall cliff, what would be a reasonable domain and range?
552 Saxon Algebra 1