algebra

6. Find the equation of each parabola described below.

a) parabola with vertex (0,0) and the focus (0,7)

b) parabola with focus (-3,0) and directrix x=3

c) parabola with vertex (3,3) and directrix x=-1

d) parabola with focus (-2,-1) and directrix y=5

e) ysquared=-6x translated according to ((x,y) -->(x-2,y+4))

could someone help me with these??

  1. 👍 0
  2. 👎 0
  3. 👁 223
  1. You need to know the following:
    vertex at (h,k)
    if it opens up or down:
    4 a (y-k) = (x-h)^2
    a negative a opens down
    if it opens right or left:
    4 a (x-h) = (y-k)^2
    a negative a opens left
    distance vertex to focus = a
    distance vertex to directrix = a
    ALWAYS SKETCH THEM
    ================================
    for example a is vertex (0,0) so h = k = 0 and focus (0,7)
    the sketch shows it with axis along the y axis opening up and distance a = 7
    so
    4 * 7 * y = x^2
    or y = x^2/28

    1. 👍 0
    2. 👎 0
    posted by Damon
  2. Note that the vertex is halfway between the focus and the directrix by the way.

    1. 👍 0
    2. 👎 0
    posted by Damon

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    A parabola has the equation y = 4(x-3)^2-7 Choose 2 true statements: A) The parabola has a minimum value B) The parabola has a maximum value C) The parabola does not cross the y-axis D) The parabola does not cross the x-axis E)

    asked by claudia on May 15, 2007
  2. math

    A parabola has the equation y = 4(x-3)^2-7 Choose 2 true statements: A) The parabola has a minimum value B) The parabola has a maximum value C) The parabola does not cross the y-axis D) The parabola does not cross the x-axis E)

    asked by claudia on May 14, 2007
  3. MATH! Urgent

    umm suppose a parabola has a vertex at (0,2) and points (1,1) how would I derive the equation and focus, i've been trying to understand this for so long, I can't get it. Does this parabola have the equation (y-2)^2 = x and a focus

    asked by sally on November 2, 2006
  4. MATH

    a. Write an equation compared to the equation of the standard parabola that satisfies the description of each parabola. 1. A parabola whose vertex is (0, -3) 2. A parabola whose vertex is (5, 1) 3. A parabola that opens down and

    asked by NAMELESS on December 31, 2018
  5. Alg II/Trig

    A parabola has a vertex at (0,0); a horizontal axis; and the point (12,6) is on the parabola. Write the equation of the parabola in standard form.

    asked by Sara on February 22, 2009
  1. ALGEBRA 1

    Please check for me.Without drawing the graph of the given equation determine (a)how many x-intercepts the parabola has (b)whether it vertex lies above, below or on the axis. 1. y=x^2-5x+6 I use the determinant sqrt b^2 -4ac

    asked by DANIELLE on April 24, 2007
  2. ALGEBRA 1

    Please check for me.Without drawing the graph of the given equation determine (a)how many x-intercepts the parabola has (b)whether it vertex lies above, below or on the axis. 1. y=x^2-5x+6 I use the determinant sqrt b^2 -4ac

    asked by DANIELLE on April 24, 2007
  3. Algebra

    The vertex of a parabola represented by f(x)=x^2-4x+3 has coordinates of (2,-1). Find the coordinates of the vertex of the parabola defined by g(x)=f(x-2). Explain how you arrived to your answer. My question: Would you move the

    asked by Anon on May 2, 2016
  4. pre cal

    What is the center of the conic whose equation is x^2 + 2y^2 - 6x + 8y = 0 2.Which one of the following equations represents a hyperbola? (5 points) A) 3x^2 + y^2 + 12x - 7 = 0 B) 3x^2 + 3y^2 + 12x - 7 = 0 C) 3x^2 + y + 12x - 7 =

    asked by Mecie on April 16, 2012
  5. Pre - Cal

    1. Find the vertex of the parabola: 4y^2+4y-16x=0 2. Find an equation of the parabola, opening down, with vertex (-3,1) and solution point (4,-5). 3. The main cables of a suspension bridge are 20 meters above the road at the

    asked by Veronica on May 5, 2014

More Similar Questions