Writing Equations
Write the equation of the function g(x) whose graph represents the indicated transformation of the function f(x)=4x+3; g(x) has undergone a vertical shrink by a factor of 1/3.
g(x)=4/3x+12
Solve for k.
|k+8|>2
k>-6 or k<-10
Graph f(x)=2x-2
Describe the transformation from f(x)=x
Transformation: Vertical stretch by a factor of 2, translated down 2.
x2 - 2x=0
x=0,2
Simplify:
i23
-i
Write the equation of the function g(x) whose graph represents the indicated transformation of the function f(x)=|3x|+2; g(x) has undergone a horizontal shrink by a factor of 1/3.
g(x)=|9x|+2
Solve for x.
|x+4|+7=3
No solution.
Graph f(x)=|x-2|+3
Describe the transformation from the graph f(x)=|x|
Transformation: Translated to the right 2, up 3.
x2 +4=0
x= 2i, -2i
Identify the focus, directrix, and axis of symmetry:
y=1/12x2
Focus: (0,3)
Directrix: y=-3
AoS: x=0
Write the equation of f(x) given that the vertex of f(x) is (2,-3) and f(x) passes through the point (6,4)
f(x)=7/16(x-2)2 -3
|b+3|=|2b-2|
b=5, b=-1/3
Graph f(x)=(x+2)2 +4
Label the vertex and axis of symmetry.
Vertex=(-2,4)
AoS: x=-2
Solve for h by completing the square:
h2-10h-4=0
h=5+sqrt(29), 5-sqrt(29)
Find a possible pair of integer values for a and c such that the following quadratic has two imaginary solutions.
ax2-5x+c=0
Any a,c such that:
25-4ac<0
Write the equation of f(x) given that f(x) has x-intercepts of 10 and 6, and f(x) passes through the point (11,8).
f(x)=8/5(x-10)(x-6)
Solve for x and y.
2x+y=5
x-y=1
(x,y)=(2,1)
Graph f(x)=-x2+2
Label the vertex and axis of symmetry.
Vertex: (0,2)
AoS: x=0
Solve for x.
(x-3)2=25
x=8, -2
Simplify:
sqrt(-49/9)
7/3i
Write the equation of f(x) given that f(x) has a focus at (0,2) and a vertex at (0,0)
f(x)=1/8x2
Solve for x, y, and z.
y=-3
2x+y=5
x-2y+z=6
(x,y,z)=(4,-3,-4)
Graph f(x)=-x2 -2x +1
Label the vertex and axis of symmetry.
Vertex: (0,1)
AoS: x=1
Solve for x using the quadratic formula.
2x2-2x-4=0
x=-1,2
Find the value of c that makes the expression a perfect square trinomial:
y2+26y+c
c=169