Show:
Writing Quadratic Functions
Focus and Directrix
Systems With Quadratics
Transformations
Inverses
100
What is the general form for vertex form of quadratic functions?
y = a (x - h)^2 + k
100
Write the equation of the parabola with a focus of (0,8) and a directrix of y = -2?
1/20x^2+3
100
Solve the following system: f(x) = -4x + 5 g(x) = 2x^2 - 7x + 3
(-1/2, 7) and (2, -3)
100
What does the value of h do to the quadratic function?
shifts it left or right
100
Find the inverse of f(x) = x^2 - 2
The inverse is -Square Root (x+2)
200
What key feature(s) of a graph do you need to write the equations for the graph in vertex form?
Vertex and a point on the graph
200
Write the equation given the focus at (1,2) and a directrix at y = -3.
y= 1/10 (x-1)^2 - 1/2
200
Solve the following system: f(x)= 54x^2 + 208x - 308 g(x)= -2x - 8
(10/9, -92/9) and (-5,2)
200
What does the value of k do to the quadratic function?
shifts it up or down
200
Find the inverse of f(x) = -x^2 - 2.
The inverse is Square Root (-x-2)
300
Given the vertex of (2, -5) and a y-intercept of -3. What is the a value of the parabola?
1/2
300
Write an equation for the parabola with a vertex at (3, -2) and a focus at ( 3, -6).
-1/16 (x - 3)^2 - 2
300
Solve the system: y = -x^2 + 9 y = x^2 + 1
(2,5) and (-2,5)
300
The function r(x) = -(x - 2)^2 - 6. The function m(x) = r(x + 7) +10. What is the new vertex form of m(x)?
m(x) = -(x + 5)^2 +4
300
Find the inverse of x^2 + 6x + 4
The inverse is -3 +/- Square Root (x+5)
400
Given the vertex of (4,3) and a second point of (3,6), what is the equation of the parabola in vertex form?
y = 3(x - 4)^2 +3
400
Write the equation given the focus at (0, -1/32) and the directrix at y = 1/32
y=-8x^2
400
Solve the following system: f(x) = -x^2 - 3x + 12 g(x) = 2x^2 + 6x
(-4,8) and (1,8)
400
The function g(x) = 2x^2 + 3 is transformed into k(x) = g(x - 2) +4. Write the function for k(x) in standard form.
k(x) = 2x^2 - 8x + 15
400
Find the inverse of g(x) = -(x - 6)^2 -3
6 +/- Square Root (x - 3)
500
Given the vertex (-1,5) and the y-intercept of 2, what is the equation of the quadratic in standard form?
y = -3x^2 -6x +2
500
Write the equation of the parabola given the focus at (8, 71/8) and the directrix at y = 73/8.
y = -2(x - 8)^2 + 9
500
Find the x-values of the following system: f(x) = -3(x - 4)^2 + 12 g(x) = (x + 2)^2 - 13
(5+/-iSquareRoot2)/4
500
The function h(x) = -2(x - 6)^2. It is transformed into the function h(x) = -1/2h(x)+2. Write h(x) in vertex form.
h(x) = (x-6)^2 +2
500
Find the inverse of h(x) = 27/5 (x - 1/3)^2 - 5
-1/3 +/- Square Root (x + 25/27)