Linear Equations & Inequalities
Look at the Graph!
Axis of Symmetry & Vertex
Parent Functions & Transformations
Systems of Equations & Inequalities
100
What is the equation for the graphed line?
y = 1/2x - 3
100
Identify the y-intercept. What is the domain and range of the function?
(0,-4) or y= -4
Domain: R
Range: y < 5
100
The Axis of Symmetry of the equation
y=-2(x-5)^2+3
is
A. x=-2 B. x=5 C. x=3 D. Another value
B. The AOS is the same as the x-value of the vertex.
100
What does the a value tell us about the graph of the equation?
y= a(x - h)2 + k
The a value is the slope. It tells us which direction the parabola will open (concave up or down).
100
Solve Using Graphing:
y = 5/3x + 2
y = -3
200
Graph the linear equation.
2x - 3y = 6
y = 2/3x - 2
200
Identify the vertex. Is the vertex a maximum or a minimum?
Vertex: (0, 0)
Minimum at y=0
200
Identify the vertex of the equation
y = 3(x - 7)2 + 1
(7, 1)
200
Graph the absolute value function using its transformations.
f(x) = - |x - 3| - 2
200
Solve the systems of equations using substitution:
y = -2x - 9
3x -6y = 9
(-3, -3)
300
Write the equation of the line with a slope of 4 that passes through the point (3, -5).
b = -17
y = 4x - 17
300
Identify the vertex. What is the axis of symmetry?
Vertex: (4,2)
AOS: x = 4
300
Identify the vertex. Is the quadratic concave up or down?
y=-3(x+1)^2+6
(-1,6)
300
Identify the parent functions and its transformations.
y= - (x - 3)2 + 1
Quadratic
Up 1, Right 3, Slope -1/1 (Concave Down)
300
Is the point (3, -4) a solution the the system of inequalities?
No. The solution works for the red area, but is on the blue dotted line.
400
Write the equation of the line that passes through the points (3, -2) and (4, -6).
y = -4x + 10
400
Would the graph of this equation have a maximum or a minimum?
y=-x^2+2x-4
maximum... since a is negative, the graph will be concave down
400
Find the vertex and axis of symmetry in the equation
y = x2 -8x + 7
x = 4
Vertex: (4, -9)
400
Write the equation for a square root function that is shifted to the left 7 units and down 2 units.
Simplify:
\sqrt{x+7}-2
400
Solve the systems of equations using Elimination:
-15x + 6y = -36
4x - 3y = 11
(2, -1)
500
Graph the linear equation.
2x - 3y > 6
y < 2/3x - 2
Dotted Line, Shade Below
500
How many zeros does this graph have? Approximately what are these zeroes?
2 (where the graph touches the x-axis)
x is about -1 and -5
500
Find the vertex of the equation
y = -5x2 + 20x + 3
(2, 23)
500
Write the equation of the cubic function that is reflected over the x-axis, shifted right 5 units, up 8 units, and vertically stretched by a factor of 7.
f(x) = -7(x - 5)3 + 8
500
Solve the systems of equations using any method:
-8x + y = -7
16x - 2y = 14
Infinitely Many Solutions