Day 11~ Day Quarterly Review Warm-Up
A ball is thrown from a building. The height of the ball as a function of time can
be modeled by the function h(t) = -16t 2 + 64t + 80, where his the height of
the ball in feet after t seconds
r.,. \ ) ~ a.
y
t W'
What is they-intercept? What poes it mean in terms of the problem
situation?
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b. What is the maximum height that the ball reaches?
1,1:-/C.,w~'f(z_')+ ~ : '-fJ I'-{_ )
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-tt,~ +- l L lf +8'='
. I1
C , ~-:1. When does the p,all reach the maxi
he'ghf'?
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" .. -b - -'9:s
= -~"f
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d. How long does it ta ke for tne ball to it the ground?
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/
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-t lo'/-L -1--l"b
o=·l<.,(t2- -'4~ -s)
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t -
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HW: Day 118 Discriminant Worksheet
Day 118 Notes -The Discriminant
S'O\ \)f
The discriminant of a quadratic function DOES NOT
the equation .
Instead, it tells you the number of X -·u,-\- er~±sthe parabola has. Remember that
x-intercepts are often referred to as
or the
.s\lt.t:b_b\fl. r
~.eJDS
Discriminant = b 2 - 4ac
Positive Discriminant
Ex. y = 2x 2
a.-:
-
7x - 2
a
b'2 - 4 a.c.
b '; .-,
C:
-:t
(-i)~ -4(~J(-2\
@)
Negative Discriminant
Ex. y = -3x 2
+x -
5
().: -3
b1 -4a..t
( , ) -i _ Lf (-3)( -sl
b=
c= er.- -s
Zero Discriminant
Ex. y
= 2x 2 -
Bx
""
v · ., •.it reo..:.-1..,.
'""\
- ' ,O "- r~ SblU'TlOi\ S )
0
+8
reo.\ \
solu11()'\}
.
Day 119 Solving Using the Quadratic Formula
-'> c\\ S<,.,\(l\J.. (\Cl.A.~
Let's practice plugging an equation into this formula!
~ =x -4x+})
2
a=
I
b
=-'1
C
=;).
X
Once, you have all of your values plugged into the formula, it is really easy to do all of math that
is ,NOT i~ the
Ins lC:iR
rad\ c.a.Q.
without a calculator. Use your calculaf ; 5
do the math that is
the radical.
x=
'i
\i.~
S iO'V
Next, check to see if you
Last, check to see if you can _ g::;..·~ ~__.,~
±~ ~
~
~
<
"J..
"1--
1--
the radical.
the three numbers outside the radical. If there
are not three numbers to simplify, th ~n it
')..
±
\
~ ....-
or
~,,J3f:>c J
Quadratic Equation:
y
= ax 2 +bx+ c
Discriminant:
b2 -4ac
Solution(s):
Quadratic Formula:
If+, 2 real solutions
If -,~ ~solutions
If 0, 1 real solution
-b +vb 2 - 4ac
x=
2a
x-.:(. (-5}~J(- SJ~ -Y (i\ ~~
=
a -= ~
2x 2 -
y
'f .-(.;i (~))
Sx - 3"
@
b = -5
C::-
(-SJ?. ·'1(11(-3)
·3
J ·re.~
St)\\A.iiOn)
)(~ ~:t ( 4q~
'i
:.
5-t1
..:::---:--
'1
I.. I\
5~, l'2- 3
?~-=-~
f.f
'-f
~2-:?:-t \:~)
i-
-
y
= 2x 2 -
Bx+ 11
y
= 4x 2 -
12x + 9
Name=-~~~~~~~~~~~-~~-~
Date: _ _ _ _ _ _ _ _ __
Period: - - -
Day 118 Discriminant Homework
'Jvhat is the equation to find a d i s c r i m i n a n t ? - - - - - - - - - - - - - - - - - - - 2) What does the discriminant tell us? Explain all three situations (positive, zero, negative).
Determine the number of zeros by using the following graphs.
3)
For each of the following determine the discriminant and explain what the discriminant means(# of solutions).
4) 3x 2
-
Bx + 4 = 0
5) -x 2
+ 6x -
6) 8x 2
-
3x
+6 = 0
7) 2x 2
+ 4x + 10 = 0
9= 0