Inequalities
Will y > x + 3 have a solid or dashed line
dashed line
Describe where the vertex would be and which direction the absolute value opens from the function.
f(x) = -|x - 4| + 9
Vertex is at (4,9) and opens down
+9 and -9
How do you determine where a function is positive and where it is negative?
Positive above the x-axis and negative below the x-axis using the x values to identify the changes
What does the shaded region of an equalities graph tell you?
The shaded region contains the answers that will make your inequality true
Describe where the vertex would be and which direction the absolute value opens from the function.
f(x) = -|x - 4| - 9
Vertex will be (4, -9) and will open down
Solve 3x2 = 75
+5 and -5
If you have a parabola that opens from the top and has a vertex of (5,-3), identify the decreasing and increasing characteristics.
Decreasing when x < 5 and Increasing when x > 5
What is the solution to this inequality?
3|c + 2| <= 9
- 5 <= c <= 1
Describe where the vertex will be and which direction the absolute value opens from the function.
f(x) = |x - 4| + 9
Solve (x - 2)2 = 49
+9 and -5
The absolute value function f has a range of (-2,oo), and a graph that is symmetric about the line x = 4, and has a y-intercept of 4. Identify the vertex and whether it opens up or opens down.
Vertex (4, -2) and opens up
What is the solution to this inequality?
|3y| - 4 > 8
y < - 4 or y > 4
The graph of f(x) = (x - 5)2 + 2 and the graph of g(x)= (x - 3)2 + 2. Describe the transformation.
The graph of g is a horizontal translation 2 units left of the graph of f.
Solve (x + 5)2 = 4 using square roots.
- 3 and - 7
Identify the vertex and which direction the parabola opens from the graph of f(x) = (x - 1)2 + 2.
Vertex is (1,2) and opens up
Will the graph that represents y > 2x2 + 3x + 1 with a vertex of (-0.75, -0.125) be shaded inside the dashed parabola, inside the solid parabola, outside the dashed parabola or outside the solid parabola?
inside the dashed parabola
Describe the transformation from the graph of f to the graph of g.
x -2 -1 0 1
f(x) 3 0 -5 -12
g(x) -3 -6 -11 -18
The graph of g is a vertical translation 6 units down of the graph of f.
Solve (x + 9)2 = 25
-4 and -14
If f is increasing over the interval (5,oo), f is decreasing over the interval (-oo, 5) and range of f is [-3,oo), Identify the vertex and if the absolute value opens up or down.
(5, -3) and up