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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
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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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

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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
x
2a
Get into standard form first.
Find values for a, b, and c, and substitute
into the formula
Simplify and reduce, if possible.
1
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
PRACTICE!
Solve using the most appropriate method.
1. 4x2 – 7 = 3(x2 – 6)
2. 50x2 – 242 = 0
4. 5x2 + 3 = 4x
5. x2 – 14x + 28 = 0
3. 6x2 + 19x + 15 = 0
6. 2(x + 5)2 – 9 = 39
2
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.
8.
7.
1  4i
5 6
4


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
13) Graph each of the following and label the vertex, axis of symmetry, and zeros.
1
 x  4  x  2
2
a) f (x)  2 x  3  5
b) g ( x )  2 x 2  6 x  5
c) y 
Solve.
14. x2 – 36 = 0
15. x2 + 8x + 16 = 0
16. 3x2 + 7x = -4
2
3
17. 14x2 – 21x = 0
18. 9x2 = 100
19.
1
(x  3) 2  7
5

20. x2 – 7 = 29
21. 2x2 + 11 = -37
Simplify.
1
23.
5 6
24.
3 7
2  10


26. (9 – 2i) (-4 + 7i)
25.
18
11
28.
5
1 i

27.

22. 5x2 + 33 = 3
7  5i
1  4i

4