Factoring
2x2 + 6x
2x(x+3)
What are a, b, and c in this quadratic expression?
4x2 + 5x - 9
a=4, b=5, c=-9
Solve the following equation: (Hint: Remember that quadratic equations typically have two solutions!)
2x2 = 32
x=4, x=-4
Add the following complex numbers:
(3 + 4i) + (4 + 8i)
7 + 12i
What is the equation for the quadratic parent function?
y = x2
x2 + 15x + 56
(x+7)(x+8)
Find the x-coordinate of the vertex for the following parabola:
y = 2x2 - 16x + 6
h = 4
Solve the following quadratic: (Hint: Remember that quadratics typically have two solutions!)
0 = 2(x - 1)2 - 18
x=4, x=-2
Multiply:
(3 - 2i)(6 + 3i)
24 - 3i
Use quadratic regression to find a model that fits the following points:
(1, 2)
(2, 16)
(3, 20)
y = -5x2 + 29x - 22
x2 - 13x + 36
(x-9)(x-4)
Find the vertex of the following parabola:
y = x2 - 6x + 8
Vertex: (3, -1)
Solve using the zero product property:
(2x + 20)(x - 5) = 0
x=-10, x=5
Multiply:
(4 - 8i)(7 - 5i)
-12 - 76i
Write the equation of the quadratic with vertex (2, -4) and a point on the graph (-3, 1).
y = 1/5(x - 2)2 - 4
2x2 + 21x + 40
(2x+5)(x+8)
List the transformations from the parent function: (Hint: stretch/flip, left/right, up/down)
y = -1(x - 3) - 2
Reflection over x-axis
Right 3
Down 2
Solve the quadratic by factoring:
y = x2 + 14x + 48
x=-6, x=-8
Solve the following quadratic:
y = 3x2 + 27
x=3i, x=-3i
Write the following equation in vertex form:
y = 2x2 - 8x + 12
y = 2(x - 2)2 + 4
3x2 + 26x + 35
(3x+5)(x+7)
Graph the following parabola. Include the vertex, y-intercept, and show the line of symmetry.
y = x2 + 4x + 3
Vertex: (-2, -1)
Y-intercept: (0, 3)
Line of symmetry: x=-2
Solve with the quadratic formula:
y = 2x2 - 2x - 3
x = 0.5 +/- 0.5*sqrt(7)
Solve with the quadratic formula:
y = 2x2 + 4x + 13/2
x= -1 +/- 3/2i
A company's projected number of sales for a certain product is given by the following equation, where P is the number of products and x is the price:
P = -2x2 + 100x - 50
What is the maximum number of products that can be sold?
P = 1200