b Look for two factors of ac that have a sum of b.
A
a h(t) = -16t^2 + 22t +3
B
b h(t) = -(8t+1)(2t-3)
Practice makes perfect
a We are given the height of a baseball at certain times.
Time (s)
Height (ft)
0.5
10
0.75
10.5
1
9
1.25
5.5
To find the quadratic equation that models the ball's height we will use a graphing calculator. First, we have to enter the values into lists. Push STAT, choose Edit, and then enter the values in the first two columns.
Now we will calculate a quadratic regression of this dataset. To view the quadratic regression analysis,we press STAT, scroll to right to view the CALC options, and then choose the fifth option in the list, QuadReg.
Selecting Calculate calculates the values of the quadratic regression.
Using these values we can write an equation that models the height of the baseball depending on time.
h(t) = -16t^2 + 22t +3
b We now have to factor the equation h(t)=-16t^2+22t+3. Since there are no common terms, we try to write bt as the sum of two terms with coefficients that are factors of ac and have a sum b.
ac = -16*3 ⇒ ac = -48
Since ac=-48< 0, the factors we are looking for have opposite signs. Because b=22>0, the factor with greatest absolute value is positive.
Factors of -48
Sum of Factors
-1,48
47
-2, 24
22
-3,16
13
-4,12
8
-6,8
2
Using the factors -2 and 24, we can rewrite the function.
-16t^2+22t+3 = -16t^2 - 2t + 24t_(22t) + 3
Now we can factor the function.
