Chapter 4 Review
Quadratic Equations & Functions
An equation or function is a quadratic if there is an ________ in the problem. (The
greatest exponent on the variable will be a _____.)
When graphing quadratic functions, there are 3 forms: How do you find the vertex?
y = ax2 + bx + c
Vertex:
y = a(x – h)2 + k
Vertex:
*Note: h is opposite!
y = a(x – p)(x – q) Vertex:
*Note: Graph the p and q as x-intercepts!
We spent most of our time in this chapter solving quadratic equation. All quadratics
have ______ solutions because the greatest exponent in any quadratic equation is a 2.
Factoring: Try this method first because
it is quick and easy when there are no
parentheses in the problem
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Look for a ______________ first to
reduce the quadratic.
Make sure the quadratic is in
_____________________ order.
Factor by Big X or slide and divide
(and reduce!) or difference of
squares, etc.
Set each factored part equal to 0
Solve
Completing the square: Use this method
if the leading coefficient is ______
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Get the variables on left and the
constants on right. Leave BLANKS
Half of b
Square it, and add to both sides.
Factor the left using the half of b
and simplify on the right.
Square root both sides,
remembering the ± symbol, and
finish with inverse operations
Inverse Operations: Use this method
when all the variable(s) in the problem
have a power of ________.
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Use the same steps that you’d use
with a linear equation to isolate the
______________ expression. (Solve
like normal)
________________________ both
sides. REMEMBER ______!!!!
Use inverse operations again to get
the variable by itself if necessary.
Simplify the radical! (might need i )
Quadratic Formula: Use this method
when all of the others don’t work or aren’t
convenient. (Hint: This will always work!)
b  b2  4ac
2a
Get into standard form first.
Find values for a, b, and c, and
substitute into the formula
Simplify and reduce, if possible.
x
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Other things to remember:
Complex Numbers
1. No negatives inside a square root – take it out as an i
2. Simplify the remaining square root if possible
3. Use i properties to simplify
i  1
i 2  1
i 3   1

4.
5.
6.
7.
i4  1
Simplifying i  Divide by 4; look at the remainder; no remainder is i4
Multiplying  Be sure to simplify i2 = -1
Dividing  Multiply by denominator on top and bottom OR by conjugate
SIMPLIFY AT END!!!
o No radicals or i in denominator! No fractions in radicals! (Separate!)
o Simplifying radicals and i if you have 2 terms in denominator: CONJUGATES
Extra Textbook Practice for Ch. 4:
Pg. 323 Chapter 4 Review Test in book
By topic
Graphing:
pg. 240 #3, 19, 20, 21, 22, 23,35, 36, 39, 40, 41
pg. 249 #3, 5, 11, 13, 15, 18, 22, 25, 27, 33, 34
Solving by Factoring:
pg. 256 #25 - 31 odd, 59, 61
pg. 263 #33 - 45 odd, 51, 53, 57, 69
Complex Numbers:
pg. 279 #3 - 11 odd, 12 - 16 even, 21, 22 - 32 even, 55
Completing the Square:
pg. 288 #4 - 16 even, 19, 23 - 33 odd, 34, 35, 41 - 43, 54
Quadratic Equation:
Pg. 296 #3 – 6, 9, 12, 14 – 20 even, 35, 36, 52 – 55, 69, 70
Ch. 4 Review:
Pg. 318 #6, 9, 13, 14, 20, 22, 25 – 35 odd, 34, 38 – 41;
Pg. 326 #1, 3, 6 – 13, 16, 22
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PRACTICE!
Solve using the most appropriate method.
1. 4x2 – 7 = 3(x2 – 6)
2. 50x2 – 242 = 0
3. 6x2 + 19x + 15 = 0
4. 5x2 + 3 = 4x
6. 2(x + 5)2 – 9 = 39
5. x2 – 14x + 28 = 0
Simplifying: No radicals, real or imaginary, may be in the denominator of a fraction.
Also there should be no _____________________factors in the radicand of a square
root. Take out all negatives. Separate if needed.
8  5i
8 2
245
9.
7.
8.
1  4i
4
5 6


Graphing: Pay attention to the form when graphing. Use it to help you find some
quick, convenient points on the graph.
10. y = -(x – 3)2
11. y = (x + 4)(x – 1)
12. y = x2 – 2x + 3
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More Practice!
13) Graph each of the following and label the vertex, axis of symmetry, and zeros.
a) f (x) 2x3 5
b) g(x) 2x2 6x5
2
c) y 
1
 x  4 x  2
2
Solve.
1. x2 – 36 = 0
2. x2 + 8x + 16 = 0
3. 3x2 + 7x = -4
4. 14x2 – 21x = 0
5. 9x2 = 100
6.
1
(x  3) 2  7
5

7. x2 – 7 = 29
8. 2x2 + 11 = -37
Simplify.
1
10.
5 6
11.
3 7
2  10
13. (9 – 2i) (-4 + 7i)
14.

12.
18
11
15.
5
1 i


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9. 5x2 + 33 = 3
7  5i
1  4i

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