# ANALYZE THE EQUATION OF A PARABOLA WORKSHEET

Write the following in standard form. Identify the

• Vertex
• Focus
• Axis of symmetry
• Direction of opening of parabola.
• Equation latus rectum and directrix
• Draw the graph

Problem 1 :

y = 3x2 + 24x + 50

Solution

Problem 2 :

-6y = x2

Solution

Problem 3 :

3(y - 3) = (x - 6)2

Solution

Problem 4 :

-2(y - 4) = (x - 1)2

Solution

Problem 5 :

4(x - 2) = (y + 3)2

Solution

1)

 Vertex (h, k) ==> (-4, 2) Focus (h, k + a) k + a = 2 + (3/4)= 11/4(-4, 11/4) Equation of latus rectum y = k + ay = 11/4 Equation of directrix y = k - ay = 2 - (3/4)y = 5/4 Axis of symmetry x = -4 Equation of directrix 4a = 3 units

2)

 Vertex (h, k) ==> (0, 0) Focus (0, -a) (0,-3/2) Equation of latus rectum y = -ay = -3/2 Equation of directrix y = ay = 3/2 Axis of symmetry x = 0 Equation of directrix 4a = 6 units

3)

 Vertex (h, k) ==> (6, 3) Focus (h, k + a) k + a = 3 + (3/4)= 15/4(6, 15/4) Equation of latus rectum y = k + ay = 15/4 Equation of directrix y = k - ay = 3 - (3/4)y = 9/4 Axis of symmetry x = 6 Equation of directrix 4a = 6 units

4)

 Vertex (h, k) ==> (1, 4) Focus (h, k - a) k - a = 4 - (1/2)= 7/2(1, 7/2) Equation of latus rectum y = k - ay = 7/2 Equation of directrix y = k + ay = 4 + (1/2)y = 9/2 Axis of symmetry x = hx = 1 Equation of directrix 4a = 2 units

5)

 Vertex (h, k) ==> (2, -3) Focus (h + a, k) h + a = 2 + (1/4)= 9/4(9/4, -3) Equation of latus rectum x = h + ax = 9/4 Equation of directrix x = h - ax = 2 - (1/4)x = 7/4 Axis of symmetry y = ky = -3 Equation of directrix 4a = 1 unit

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