Transformations of Quadratic Functions
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
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
Where does the vertex lie in relation to the focus and directrix?
The middle. Equal Distance from both locations.
Describe the transformation of f(x)=x^2 represented by g. g(x)=(x-5)^2 - 3
What is a translation 5 units right and 3 units down.
Write a rule for g(x) if f(x)=x^2 reflection over the x-axis and vertical shrink by a factor of 2/3
What is g(x)=-3/2 x^2
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
If the focus is (2,3) and the directrix is y=-5, what is the vertex?
(2,-1)
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 and reflection over the x-axis
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
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)
Write the equation for a line whose vertex is (-3,-1) and whose focus is (-3,4)
(x+3)^2=20(y+1)
Describe the transformation of f(x)=x^2 represented by g. g(x)=-(x-7)^2 +2
What is a reflection over the x-axis and translation 2 units up and 7 units right.
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
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
When priced at $40 each, a toy company sells 5000 toys. The manufacturer estimates that each $1 increase in price will decrease sales by 100 units. Find the unit price of a toy that will maximize the total revenue, along with what the maximum revenue achieved.
4500 toys, $45, $202,500
If the focus is (6,2) and the directrix is x=-2, what is the equation of the line?
(y-2)^2=16(x-2)
Describe the transformation of f(x)=x^2 represented by g. g(x)=-1/2(x + 2)^2 -1
What is a reflection over the x-axis, a vertical shrink by a factor of 1/2, a translation 2 units left and 1 unit down.
Write a rule for g(x) if f(x)=x^2 Vertical shrink by a factor of 3, translation down 6, and right 4, reflection over the x-axis.
What is g(x)= -3(x - 4)^2 - 6
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+5)^2+3
What is Domain: All reals Range: (-inf, -23] Increasing: x<2 Decreasing: x>2 Maximum at: -23
The function f(x)=-0.02(x-30)^2+18 models the path of a football kicked by a player, where x is the horizontal distance (in yards) and y is the height (in yards). The player kicks the ball a second time so that it travels the same horizontal distance but reaches a maximum height that is 8 yards less than the maximum height of the first kick. Write a function that models the path of the second kick.
What is f(x)=-0.02(x-30)^2+10
What is the equation of a line whose focus is at (-3,3) and directrix is x=1
(y-3)^2=-8(x+3)