Describe the transformation of f(x)=x^2 represented by g.
g(x)=(x+4)^2
What is a translation 4 units left.
100
Write a rule for g(x) if f(x)=x^2
Translation down 2 and to the left 3
What is g(x)= (x+3)^2 - 2
100
Find the vertex and axis of symmetry. Sketch a quick graph.
f(x)=3(x-2)^3 +5
What is vertex: (2,5) axis of symmetry x=2
100
Write an equation for the parabola with the given characteristics in vertex form.
vertex: (10,-4)
passes through: (1, -22)
What is f(x)= 2(x-10)-4
100
Describe the transformation of f(x)=x^2 represented by g(x).
g(x)= -1/2(4x+1)^2 -4
What is
reflection over the x-axis
Vertical shrink by a factor of 1/2
Horizontal shrink by a factor of 1/4
Translation 1 unit left and 4 units down
200
Describe the transformation of f(x)=x^2 represented by g.
g(x)=x^2 - 3
What is a translation 3 units down.
200
Write a rule for g(x) if f(x)=x^2
Horizontal shrink by a factor of 2/3
What is g(x)=(3/2 x)^2
200
Find the vertex and the axis of symmetry. Sketch a quick graph.
f(x)= -2x^2 +16x +3
What is vertex: (4, 35) axis of symmetry: x=4
200
Write an equation for the parabola with the given characteristics in vertex form.
Vertex: (2,3)
Passes through: (1,6)
What is f(x)=-3(x-2)+3
200
Write a rule for g.
Translation up 3 units and to the right 2. Horizontal shrink by a factor of 3, and a reflection over the y-axis.
What is
g(x)=(-1/3x -2)^2 +3
300
Describe the transformation of f(x)=x^2 represented by g.
g(x)=3x^2
What is a vertical stretch by a factor of 3
300
Write a rule for g(x) if f(x)=x^2
Translation 2 units left, 3 units up, reflection over the y axis
What is g(x)= (-x+2)^2 +3
300
Find the vertex, axis of symmetry and x-intercepts. Sketch a quick graph.
f(x)= 2(x-2)(x-6)
What is
x-intercepts: (2,0) (6,0)
a.o.s.: x=4
vertex: (4, -8)
300
Write an equation for the parabola with the given characteristics in intercept form.
Passes through: (4,3)
X-intercepts: (-1,0) (5,0)
What is
f(x)=-3/5 (x+1)(x-5)
300
Label the vertex, the axis of symmetry, and x-intercepts and sketch a quick graph.
f(x)=(x-3)(x+7)
What is
vertex: (-2,-25)
a.o.s.: x=-2
x-intercepts: (3,0) (-7,0)
400
Describe the transformation of f(x)=x^2 represented by g.
g(x)=(x-7)^2 +2
What is a translation 2 units up and 7 units right.
400
Write a rule for g(x) if f(x)=x^2
Vertical stretch by a factor of 2, reflection over the x-axis, translation 3 units left, and 2 units down.
What is g(x)=-2(x+3)^2 -2
400
State the domain and range. Find where the function is increasing and decreasing. State whether the function has a maximum or a minimum and where it is.
f(x)= 2(x+4)^2 - 2
What is What is Domain: All reals
Range: [-2, inf)
Increasing: x> -4
Decreasing: x<-4
Minimum at -2
400
Write an equation for the parabola with the given characteristics in intercept form.
passes through: (0,-32)
x-intercepts:(-1,0) (8,0)
What is
f(x)=4(x+1)(x-8)
400
State the domain and range. Find where the function is increasing and decreasing, and state whether the function has a maximum or a minimum and where it it located.
f(x)=-3(x-1)^2 +5
What is
Domain: All reals
Range: (-inf, 5]
Increasing: x<1
Decreasing: x>1
Maximum at 5
500
Describe the transformation of f(x)=x^2 represented by g.
g(x)=-3( 1/2 x + 2)^2 -1
What is a reflection over the x-axis, a vertical stretch by a factor of 3, a horizontal stretch by a factor of 2, a translation 2 units left and 1 unit down.
500
Write a rule for g(x) if f(x)=x^2
Horizontal shrink by a factor of 3, translation down 6, and right 4, reflection over the x-axis.
What is g(x)= -(1/3 x - 4)^2 - 6
500
State the domain and range. Find where the function is increasing and decreasing. State whether the function has a maximum or a minimum and where it is.
f(x)= -2x^2 -8x +1
What is
Domain: All reals
Range: (-inf, -23]
Increasing: x<2
Decreasing: x>2
Maximum at: -23
500
Write an equation for the parabola with the given characteristics in vertex form and intercept form.
passes through: (0,-20)
x-intercepts: (5,0) (-1,0)
What is
f(x)=4(x-5)(x+1)
f(x)=4(x-2)^2 -36
500
Write an equation for the parabola with the given characteristics in vertex form and intercept form.
passes through: (0, -48)
x-intercepts: (-2,0) (8,0)