Characteristics of Quadratics
Using the diagram shown to you by your teacher, identify the interval of increase.
(-infinity,2)
Solve the following quadratic equation by factoring: x2 - 4 = 0
x = 2 x = -2
Solve the following quadratic equation by completing the square: x2 + 6x = -8
x = -2 , x = -4
What is the quadratic formula?
x = -b +- sqrt(b2 - 4ac) /(2a)
Name the four methods for solving quadratic equations.
Completing the Square
Factoring
Quadratic Formula
Square Root Method
Using the diagram shown to you by your teacher, identify the roots of the quadratic. List them as ordered pairs.
(0,0) and (4,0)
Solve the following quadratic equation by factoring:
9x2 - 81 = 0
x = -3, x = 3
Solve the following quadratic equation by completing the square: x2 - 6x = -5
x = 1, x = 5
Solve the following quadratic equation by using the quadratic formula: x2 + 6x + 5 = 0
x = -1, x = -5
When calculating the discriminant what does each type of answer mean about the quadratic's solution(s)?
a) a positive answer
b) a negative answer
c) an answer of 0
a) a positive answer-TWO REAL SOLUTIONS
b) a negative answer-NO REAL SOLUTION
c) an answer of 0-ONE REAL SOLUTION
Use the diagram shown by your teacher to identify the axis of symmetry.
x = 2
Solve the following quadratic equation by factoring: 4x2 - 400 = 0
x = 10 , x = -10
Solve the following quadratic equation by completing the square: 2x2 - 4x = 48
x = -4 x = 6
Solve the following quadratic equation by using the quadratic formula: x2 - 9x + 6 = 0
x = (9 +/- sqrt 57) / 2
What is the formula for calculating the discriminant?
b squared minus 4ac
What do we know about the a value of the quadratic forming this parabola?
it is a negative number
Solve the following quadratic equation by factoring: x2 - 9x = -8
x=8 or x=1
Solve the following quadratic equation by completing the square: x2 + 10x +5 = 0
x = -5 +/- 2sqr5
Solve the following quadratic equation by using the quadratic formula: 2x2 + 9x + 4 = 0
x = -1/2 x = -4
What is the standard form of a quadratic equation?
ax2 + bx + c = 0
Using the diagram shown by your teacher, what is the interval of decrease?
2, infinity
Solve the following quadratic equation by factoring: 5x2 -125 = 0
x = 5 , x = -5
Solve the following quadratic equation by completing the square (nearest tenth):
x2 - 8x + 13 = 0
x = 5.7, x = 2.3
Solve the following quadratic equation by using the quadratic formula (nearest tenth):
4x2 - 17x =-12
x = 3.4, x = .9
What is the difference between an exact answer and a decimal approximation? What form are both in?
Exact answer is either an integer, fraction or contains a square root
A decimal approximation is just that, a decimal approximating the exact answer. An approximate decimal answer from your calculator