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Math I. UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you solve quadratic equations that can’t be factored? Standard: MM2A4.b. DAY ONE. We will get x squared by itself. Then we will take the square root of both sides of the equal sign. - PowerPoint PPT Presentation
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Math I
UNIT QUESTION: What is a quadratic function?Standard: MM2A3, MM2A4
Today’s Question:How do you solve quadratic equations that can’t be factored?Standard: MM2A4.b.
Examples. Solve the equation. Write the solutions as integers if possible. Otherwise, write them as radical expressions.
5.24.1 22 nx
42 x 52 n
5n2x
Falling object model
When an object is dropped, the speed with which it falls continues to increase. Ignoring air resistance, its height h can be approximated by the falling object model:
sth 216
An engineering student is a contestant in an egg dropping contest. The goal is to create a container for an egg so it can be dropped from a height of 32 feet without breaking (s = starting height). Find the time (t) it will take for the egg to hit the ground (height = ? ). Disregard air resistance.
SOLUTION: The starting height is 32 feet.
Now, substitute 0 for h and solve.32160 2 t21632 t Subtract 32 from both sides
Divide both sides by –16 22 tTake the square root of both sides
4.12 t So, the answer is 1.4 seconds. It is only the positive of the square root b/c you can’t have negative seconds!!!!!
sth 216
The following quadratics are in standard form, ax2 + bx + c
Evaluate b2 – 4ac for each of the following
1
0
-15
1)x2 – 3x + 2
2)x2 – 4x + 4
3)2x2 – 3x + 3
There is a way to tell how many roots an equation will have.
It’s called finding the discriminant.
The discriminant is a small part of the quadratic formula.
b ac2 4
b ac2 4If the answer is POSITIVE, then you will have 2 roots.
If the answer is ZERO, then you will have 1 root.
If the answer is NEGATIVE, then you will have no roots.
Our text book says solutions instead of roots (same thing).
Quadratic Formula: gives the solution of in terms of the coefficients a, b & c.
2 0ax bx c
a
acbbx
2
42
a
The solutions of the quadratic equation are
a
a
c
c
bb
b
Ex: 1 Solve x2+ 9x +14 = 0
a
acbbx
2
42
a =
b =
c =
12
141499 2
1st
12
1414819
2nd
2
56819
2
259
2
59
2
59
2
59 and
2
14
2
4 and 7 2 and
A rocket is shot upward with an initial velocity of 125 feet per second from a platform 3 feet above the ground. Use the model to find how long it will take the rocket to hit the ground.
216h t vt s
3 ft
t = 7.83 seconds