System of Equations
A point that makes BOTH equations true is called what?
The Solution (point of intersection)
The table shows a pattern
x y
1 5
2 8
3 11
Determine whether the table represents a linear or exponential function
Increasing Linear function
When does a quadratic have no solutions?
When the graph does not touch the x-axis
Factor Completely
x2+7x+12
(x+3)(x+4)
What is the highest or lowest point on a parabola called?
vertex
t+4m=10
t=-2
(-2,3)
What is the equation of a line
y=mx+b
Solve
(x-1)(x+5)=0
x=1
x=-5
Factor completely:
x2−9x+20
(x-5)(x-4)
A ball is thrown into the air and follows a parabola. What does the vertex represent in this situation?
The maximum height
Solve the system
x+y=10
x-y=2
(6,4)
Write the equation of the line with slope m=3 passing through (2,5).
y=3x-1
Which equations have two solutions
A. x2=9
B. 7x2
C. 4x2=16
D. 5x-2=13
A and C
factor x2-400
(x+20)(x-20)
Two students throw a rock. The equations model the rock's movement.
student A equation is f(x)= (x-1)(x+2)
Student B equation is g(x)=(x+2)(x-4)
Student A
Solve the system
3x+2y=18
x+y=7
(4,3)
A line has slope m=5 and passes through (1,7). Write the equation in slope-intercept form.
y=5x+2
Solve (x-9)(2x-3)=0
x=9 and x=3/2 (1.5)
Factor completely:
x2+5x+7
Cannot be factored
Two students throw a rock. The equations model the rock's movement.
student A equation is f(x)= (x-2)(x+3)
Student B equation is g(x)=(x+1)(x-5)
5 seconds
Solve the systems
5x+2y=24
3x-2y=8
What is the value of 10x
Line t in the xy- plane has a slope of 8 and passes through the point (0,9). Write an equation that defines line t.
y=8x+9
Solve
x2+5x+6=2
x=-1
x=-4
Factor completely:
2x2+11x+5
(2x+1)(x+5)
Two students throw a rock. The equations model the rock's movement.
student A equation is f(x)= (x+2)(x+3)
6 units