CPM Homework Help : A2C Problem 11-157

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Home > A2C > Chapter 11 > Lesson 11.3.3 > Problem 11-157

11-157.

Identify the shape of the graph of each equation below, change it to graphing form (if necessary), and sketch a graph. Homework Help ✎
1. 2y² − x + 4y + 2 = 0
2. 5x + 2y − 10 = 0
3. 4x² + 4y² + 4x − 24y + 21 = 0
4. 9x² − 16y² + 54x − 32y + 29 = 0
5. 9x² + 4y² + 54x − 16y + 97 = 0
6. 4x² − y² + 24x + 36 = 0

Hint (a):

2y² + 4y + 2 = x

Answer (a):

x = 2(y + 1)²

Hint (b):

2y = −5x + 10

Hint (c):

Try to factor and complete the squares for x and y.

Hint 2 (c):

4(x² + x) + 4(y² − 6y) = −21

More Help (c):

$4\left(x^2+x+\frac{1}{4}\right)+4(y^{2}-6y+9)$

= − 21 + 1 + 36

Answer (c):

$\left(x+\frac{1}{2}\right)^2+(y-3)^2=4$

Hint (d):

See part (c).

Hint (e):

See part (c).

Hint 2 (e):

9(x² + 6x) + 4(y² − 4y) + 97 = 0

9(x² + 6x + 9) − 81 + 4(y² − 4y + 4) − 16 + 97 = 0

More Help (e):

9(x + 3)² + 4(y − 2)² = 0

Answer (e):

Hint (f):

See part (c).

More Help (f):

Notice that y ² is the only term containing y. Try to get it by itself.

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