Polynomials
What is the name of the 5 in the polynomial below:
5x2+3x-4
Leading Coefficient
Write the general equation of a quadratic in vertex form.
y=a(x-h)2+k
Factor out the GCF.
18x4y+12x3y3-6x2y5
6x2y(3x2+2xy2 -y4)
The name of the property that allows us to solve
(x-9)(x+4)=0
x-9=0. and x+4=0
Zero Product Property (ZPP)
What is the quadratic formula?
x = -b +- sqrt(b2 - 4ac) /(2a)
What is the degree of the polynomial:
2x-3x4+9-x3
Degree is 4
What does the a value tells us about the quadratic function.
Whether it opens up or down and if its wider or narrower than the parent function.
factor completely
x2+5x-14
(x+7)(x-2)
When analyzing a table of values, where do you find the solutions to the function?
The x value when the y is equal to zero.
Solve the following quadratic equation by using the quadratic formula: x2 + 5x -4 = 0
x = [-5+-sqrt(41] /2
Add and write the sum in standard form.
(x3-2x2+x-2)+(2x-5x2-1)
x3-7x2+3x-3
What is the general equation of a quadratic function in standard form AND what is the vertex?
f(x)=ax2+bx+c
Vertex: (-b/2a, f(-b/2a) )
Factor Completely
2x2+x-3
(2x+3)(x-1)
Where do solutions of quadratic equations appear on the graph of a quadratic function?
The x intercepts
What is the discriminant and what information does it give?
Subtract and write the difference in standard form.
(x3+1)-(5x-2x3+1)
3x3-5x
g(x)=(x+2)2-3
Factor completely
x2+16x+64
(x+8)2
what is a complex number?
A number with a real part and an imaginary part. The imaginary part is the result of taking the square root of a negative number.
Multiply (2-3i)(4+i)
11-10i
Multiply and write the product in standard form
(4x+1)(2x2+3x-5)
8x3+14x2+17x-5
Find the vertex and y-intercept of the quadratic below.
f(x)=2x2-8x+3
Vertex: (2,-5)
y-intercept (0,3)
Factor Completely
5x2-20
5(x+2)(x-2)
Solve by using the square root method
(x-4)2+13=9
x=4+-2i
Solve by completing the square
x2+2x+10=0
(x+1)2+9=0
x=-1+-3i