Discriminant
Identify the discriminant of:
8b^2-6b+3=5b^2
D=0
Find the axis of symmetry:
y=x^2-12x+44
x=6
Find the sum and product of the roots of the following without solving:
x^2-9x+20=0
sum = 9
product = 20
Solve and leave your solution in interval notation:
x^2-10<3x
(-2,5)
Solve:
abs(3x-2)-24=14
x=40/3, x=-12
Determine the nature of the roots of:
4k^2+5k+4=-3k
1 real root
Find the roots of the following function. Then classify them.
f(x)=-x^2+8x-20
x=-10, x=2
2 real rational unequal roots
Find the sum and product of the roots of the following equation without solving:
4x^2=4xsqrt5-5
sqrt5
5/4
Solve and leave your answer in interval notation:
x^2+8x+16>=0
(-infinity,infinity)
All real numbers
Simplify:
(3+sqrt(-4))(5-sqrt(-9))
21-i
Find the discriminant and determine the nature of the roots:
-10n^2-3n-9=-2n
D=-359
2 imaginary roots
What is the vertex of:
y=2x^2-4x-2
(1,-4)
Write a quadratic equation whose roots are -3 and 1/2
x^2+5/2x-3/2=0
Solve and leave your answer in interval notation:
-x^2+5x>=-6
[-1,6]
Simplify:
7sqrt(-8)*5isqrt(-32)*isqrt(-27)
1680isqrt3
Find the range of values for the constant k so that the equation below has 1 real root.
x^2+kx+16=0
k=+-8
Identify the x and y-intercepts of:
y=x^2+16x+64
x-intercept: -8
Y-intercept: 64
Write and equation of a quadratic whose roots are
5+-sqrt2
x^2-10x+23=0
Solve and leave your answer in interval notation:
(x+1)(x-3)^2>0
(-1,3)U(3,infinity)
Factor:
64x^3+125
(4x+5)(16x^2-20x+25)
Find the range of values of the constant k so that the graph of the equation shown below does NOT cross the x-axis:
y=x^2+5x+k
k>25/4
Identify the maximum point of the graph:
f(x)=-1/3x^2+4/3x-16/3
(2,-4)
Write an equation of a quadratic function who has one root of 3-2i
x^2-6x+13=0
Solve and leave your answer in interval notation:
x^4+4x^3-12x^2<=0
[-6,2]
Simplify:
((z^2-49)/(3z-15))/((z+7)/12)
(4(z-7))/(z-5