Download f(x) = ax 2 +bx + c - Effingham County Schools

MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
Warm Ups
Wednesday, May 24, 2017
Find the zeros of the function.
y  4 x 2  15 x  9
1.
3
x  ,x  3
4
2. y  4 x2  4 x  1
1
x
2
Find the x-intercepts
2
(x + 3) = 16
(x + 3)(x + 3) = 16
3.
2
x + 3x + 3x + 9 = 16
x 2 + 6 x + 9 = 16
x2 + 6 x - 7 = 0
(x + 7)(x - 1) = 0
x = - 7, x = 1
MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the
quadratic formula.
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
Wednesday, May 24, 2017
Essential Question:
How do we use the square root property?
MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the
quadratic formula.
2
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
Vocabulary
Square Root Property
If x  b, then x  b.
2
MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the
quadratic formula.
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
Key Concept
To solve a quadratic of the form f ( x)  ax 2  c, use the
square root property.
1. Isolate the radical.
2. Take the square root.
3. Simplify the radical.
MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the
4
quadratic formula.
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
Example
Solve the quadratic equation.
1. 2 x  3  93
2
x  3i 5
MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the
5
quadratic formula.
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
Guided Practice
Solve the quadratic equation.
2 2
2.
x 1  4
5
30
x
2
MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the
6
quadratic formula.
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
Guided Practice
Solve the quadratic equation.
3. 3x  150  282
2
x  2i 11
MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the
7
quadratic formula.
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
Guided Practice
Solve the quadratic equation.
2 2
4.
x 1  4
5
30
x
2
MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the
8
quadratic formula.
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
Guided Practice
Solve the equation.
2 2
5.
x  4  12
3
MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the
quadratic formula.
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
Key Concept
Falling Objects!
Use h = -16t2 + h0
Height of
the
object
after it
has fallen
# of seconds
after the object
is dropped
Object’s
initial
height
MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the
quadratic formula.
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
Example
6. The tallest building in the USA is in
Chicago, Illinois. It is 1450 ft. tall. How
long would it take a penny to drop from
the top of the building to the ground?
90.625  t
h  16t  h0
2
0  16t  1450
2
 1450  16t
2
2
90.625  t 2
t  9.52 seconds
MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the
11
quadratic formula.
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
7. A rescue helicopter hovers 68 feet above a jet ski in
distress and drops a life raft. The height in feet of the
raft above the water is given by h(t) = -16t2 + 68.
Determine how long it will take for the raft to hit the
water after being dropped from the helicopter.
Solution:
The raft will hit the water when its height is 0 feet
above the water. Solve h(t) = -16t2 + 68 = 0.
-16t2 + 68 = 0
-16t2 = - 68
t
2
68
=
16
Ignore the - 2.1.
WHY?
68
t=±
» ±2.1 sec
16
The life raft will
hit about 2.1
seconds after it is
dropped.
MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the
quadratic formula.
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
Model a dropped object with a quadratic function
8. Science Competition
For a science competition,
students must design a container
that prevents an egg from breaking
when dropped from a height of 50
feet. How long does the container
take to hit the ground?
Use h
0 =
– 50 =
50
16
50
+ 16
= – 16t 2 + 50
– 16t 2 + 50
– 16t 2
=
t2
=
t2
+ 1.8 ≈ t
Reject the negative solution, – 1.8, because
time must be positive. The container will fall
for about 1.8 seconds before it hits the
ground.
MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the
quadratic formula.
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
9. 2 x 2  5  5 x 2  37
MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the
14
quadratic formula.