Question

Complete the square and graph: 9y²−x − 18y +10=0 ​

Answer 1

Answer:

See below ~

Step-by-step explanation:

Completing the square :

• 9y² - x - 18y + 10 = 0
• 9y² - 18y + 9 - 9 - x + 10 = 0
• (3y - 3)² - x + 1 = 0

Graph :

Answer 2

Answer:

x = 9(y - 1)² + 1

see attached for graph

Step-by-step explanation:

Completing the square

Given equation:

9y² - x - 18y + 10 = 0 ​

As there is a y² in the equation, this implies it is a sideways parabola.

To complete the square for a sideways parabola, collect the y variable terms on the left and everything else on the right:

⇒ 9y² - 18y = x - 10

Factor out the leading coefficient from the left side:

⇒ 9(y² - 2y) = x - 10

Take the coefficient of y, half it, then square it:  (-2 ÷ 2)² = 1

Add this inside the parentheses, and add the distributed value of this to the right side:

⇒ 9(y² - 2y + 1) = x - 10 + 9

Factor the parentheses and simplify the right side:

⇒ 9(y - 1)² = x - 1

Add 1 to both sides to make x the subject:

⇒ x = 9(y - 1)² + 1

Graphing the parabola

Conic form of a sideways parabola with a horizontal axis of symmetry:

x = a(y - k)² + h

(where (h, k) is the vertex and y = k is the axis of symmetry)

If a > 0, the parabola opens to the right, and if a < 0, the parabola opens to the left.

Therefore, for  x = 9(y - 1)² + 1

• vertex = (1, 1)
• axis of symmetry:  y = 1
• a > 0 ⇒ the parabola opens to the right

To find the x-intercept, set y = 0 and solve for x:

⇒ x = 9(0 - 1)² + 1

⇒ x = 9(-1)² + 1

⇒ x = 9(1) + 1

⇒ x = 10

Therefore, the y-intercept is (10, 0)

As the axis of symmetry is y = 1, the other value of y when x = 10 is y = 2

Plot the vertex and points. Add an axis of symmetry to help draw the curve.  Draw the parabola opening to the right.

**graph attached**