Quadratics 1
What is the quadratic formula?
x=(-b+-sqrt(b^2-4ac))/(2a
In terms of quadratics equations, what is another word for solutions? (Hint: There are three possible answers)
Roots, Zeros, X-Intercepts
Simplify the following:
sqrt((100x^6)/(25x^2)
2x^2
Factor:
8x^3-1
(2x-1)(4x^2+2x+1)
If you translate function f(x) 7 units left and 3 units down, what is the resulting function? Write your answer in terms of f(x).
f(x+7)-3
Solve:
x^2+2x-80=0
x=-10 and x=8
Solve:
5x^2+12=135
x=+-5
Simplify:
sqrt(6x^2y^3)sqrt(4x^5y^7)
2x^3y^5sqrt(6x)
Factor:
x^3+7x^2-7x-49
(x^2-7)(x+7)
Sketch the graph for the function below:
y=-2abs(x-1)+3
On graph paper
Solve. Simplify your answer as much as possible, but give an exact answer.
2x^2+8x+3=0
x=(-4+-sqrt(10))/2
Solve. Simplify your answer as much as possible, but give an exact answer.
4x^2-9x+1=0
x=(9+-sqrt(65))/8
Simplify.
(5sqrt(2))/(10sqrt(4))
sqrt(2)/4
Factor:
x^4-10x^2+9
(x-3)(x+3)(x-1)(x+1)
Write an equation for a circle with a radius of 3 and a center of (5,-2)
(x-5)^2+(y+2)^2=9
What are the coordinates for the vertex for the function below?
f(x)=x^2+10x+19
(-5,-6)
Divide.
2x^2+4x-7divx-3
2x+10+23/(x-3)
Simplify:
i^212
1
Simplify:
(x-1)/(4x+8)*(x^2+5x+6)/(x^2+2x-3
1/4
What is the center and radius of the circle below?
x^2+8x+y^2-10y=40
Center (-4,5)
Radius = 9
Suppose a soccer ball is kicked 80 yards and reaches a maximum height of 50 yards. Write an equation for the parabola that models the flight path of the soccer ball.
y=-1/32(x-40)^2+50
Suppose you have a square and a rectangle. The length of the square is the same as the length of rectangle. The width of the rectangle is 4 more than the length. If the total area of the two shapes is 390, what is the length of the square?
13
Simplify:
(2i+5)(i-3)
-17-i
Simplify:
(4x^3+12x^2-20x)/(4x)
x^2+3x-5
Write the equation for the following: Take the parent graph of a root function, reflect it over the x-axis, shift it right 2 units and up 3 units.
-sqrt(x-2)+3