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If the equation is x as a function of y, then the parabola is vertically oriented.

     If the coefficient of the x² term, 'a,' is positive, the parabola opens upward.

     If the coefficient of the x² term is negative, the parabola opens downward.

If the equation is y as a function of x, the parabola is horizontally oriented.

     If the coefficient of the y² term is positive, the parabola opens to the right.

     If the coefficient of the y² term is negative, the parabola opens to the left.

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1.) x = (y - 5)² + 1

Opens to the right.

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Vertex (1, 5)

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h = 1

k = 5

a = 1

p = 1 / 4a

p = 1/4

Focus (Fx, Fy)

Fx = h + p

Fx = 1 + 1/4

Fx = 5/4

Fy = k

Fy = 5

Focus (5/4, 5), or

Focus (1.24, 5)

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2.) y = 2(x + 3)² - 4

Opens upward.

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Vertex (- 3, - 4)

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h = - 3

k = - 4

a = 2

p = 1 / 4(2)

p = 1/8

Fx = k + p

Fx = - 4 + 1/8

Fx = - 32/8 + 1/8

Fx = - 28/8

Fx = - 7/2

Fy = h

Fy = - 3

Focus (- 7/2, - 3), or

Focus (- 3.5 - 3)

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3.) y = - 2x + 1

Straight Diagonal line; no vertex; no focus.

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4.) y = x² - 6x + 10

Opens upward.

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y = (x² - 6x) + 10

y = (x² - 6x + 9) + 10 - 9

y = (x - 3)² + 1

Vertex (3, 1)

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h = 3

k = 1

a = 1

p = 1/4

Fx = h

Fx = 3

Fy = k + p

Fy = 1 + 1/4

Fy = 4/4 + 1/4

Fy = 5/4

Focus (3, 5/4), or

Focus (3, 1.25)

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5.) x = 3y² + 6y + 11

Opens to the right.

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x = (3y² + 6y) + 11

x = 3(y² + 2y) + 11

x = 3(y² + 2y +1) + 11 - 1

x = 3(y + 1)² + 10

Vertex (10, - 1)

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h = 10

k = - 1

a = 3

p = 1 / 4(3)

p = 1/12

Fx = h + p

Fx = 10 + 1/12

Fx = 120/12 + 1/12

Fx = 121/12

Fy = k

Fy = - 1

Focus (121/12, - 1, or

Focus (10.0833, - 1)

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once you position them on a graph you want to have a scale that shows the values of x and y. You study and list the values of (x, y) at 3 separate aspects call the elements (x1, y1), (x2, y2), and (x3, y3) y = a x^2 + b x + c once you position each and each and every aspect into the equation you get an equation in a, b and c. you presently have 3 equations to clean up concurrently to stumble on a, b, c.