Question

Consider the graph of 5x² + 8x + 4y² - 4y = 70.

If the graph of 5x² + 8x + 4y - 4y = 70 is stretched horizontally by a factor of 3, the equation of the stretched graph will be

If the graph of 5x² + 8x + 4y² - 4y = 70 is stretched vertically by a factor of 7, the
equation of the stretched graph will be

Answer 1

To stretch the graph horizontally by a factor of 3, we need to multiply the x-coefficient by 1/3. Similarly, to stretch the graph vertically by a factor of 7, we need to multiply the y-coefficient by 1/7. Therefore:

Horizontally stretched graph: 5(1/3x)² + 8(1/3x) + 4y² - 4y = 70

Simplifying:

(5/9)x² + (8/3)x + 4y² - 4y = 70

Vertically stretched graph: 5x² + 8x + 4(1/7y)² - 4(1/7)y = 70

Simplifying:

5x² + 8x + (4/49)y² - (4/7)y = 70