Complete the Square, Quadratic Formula and the Discriminant
100
The graph of a quadratic function is a _____________.
What is parabola?
100
Another useful form of a quadratic function is vertex form, which is _______________.
What is y=a(x-h)^2+k?
100
A number r is a ____________ of a number s if r^2=s.
What is square root?
100
A ________________________ written in standard form is a number a+bi, where a and b are real numbers.
What is complex number?
100
When you add a term to a binomial to create a perfect square trinomial, the process is called ________________________.
What is completing the square?
200
The lowest or highest point on a parabola is the ________________.
What is vertex?
200
DAILY DOUBLE!!!
If the graph of a quadratic function has at least one intercept, then the function can be represented in intercept form, which is ______________________.
What is y=a(x-p)(x-q)?
200
If you have a fraction with a square root in the denominator, to rationalize the denominator, you must multiply by the _____________________.
What is conjugate?
200
Two complex numbers of the form a+bi and a-bi are called _________________________.
What is complex conjugates?
200
The Quadratic Formula
What is x = [-b +/- sqrt(b^2-4ac)]/2a?
300
The ____________________ divides the parabola into mirror images and passes through the vertex.
What is axis of symmetry?
300
A __________ is a function with two terms and a _____________ is a function with three terms.
What is binomial and trinomial?
300
Solve using square roots:
x^2 = 84
What is x= 2sqrt(21) and x= -2sqrt(21)?
300
DAILY DOUBLE!!!!
Solve the equation:
x^2 = -28
What is x = 2i sqrt(7) and x = -2i sqrt(7)?
300
What is the discriminant formula and what does it tell you?
What is b^2-4ac, if b>0 two real solutions, if b=0 one real solution, if b<0 two imaginary solutions.
400
A quadratic function has a _______________________ if a>0 and a ___________________ if a<0.
What is minimum value and maximum value?
400
Solve the equation by factoring:
x^2-11x+30=0
What is x=5 and x=6?
400
Solve the equation using square roots:
4(x-1)^2=8
What is x = 1 + sqrt(2) and x = 1 - sqrt(2)?
400
Write the expression as a complex number in standard form:
(3+i)(5-i)
What is 16+2i?
400
Solve by completing the square:
3x^2 + 42x = -24
What is x = -7 + sqrt(41) and x = -7 - sqrt(41)?
500
Graph the function. Label the vertex and axis of symmetry.
y=3x^2-6x+4
See instructor for answer.
Vertex: (1, 1)
Axis of symmetry: x=1
500
Solve by factoring:
-3y+8 = y^2
What is y=-7 and y=4?
500
Solve by using square roots:
7(x-4)^2-18 = 10
What is x=2 and x=6?
500
Solve the equation using square roots:
9-4y^2=57
What is x = 2i sqrt(3) and x = -2i sqrt(3)?
500
Use the quadratic formula to solve the equation:
3-8v-5v^2=2v