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Writing Quadratic Functions
Focus and Directrix
Transformations
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
What does the value of h do to the quadratic function?
shifts it left or right
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
What does the value of k do to the quadratic function?
shifts it up or down
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
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
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
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
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
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