Final answer:
To change the quadratic equations to either y² = 4ax or x² = 4ay form, we need to complete the square. By rearranging the equations and simplifying, we can express them in the desired forms.
Step-by-step explanation:
To change the quadratic equations to either y² = 4ax or x² = 4ay form, we need to rearrange the equations. Let's go through each equation:
a) y = x² - 18x + 87:
Complete the square to obtain y² = 4ax form: y² + 18y = x² + 87. Rewrite the right side as (x - 43.5)² - 1350.25. Simplify the left side to get (y + 9)² = (x - 43.5)² - 1350.25. Therefore, y² = 4a(x - 43.5).
b) x = y² - 10y + 28:
Complete the square to obtain x² = 4ay form: x² - 10x = y² + 28. Rewrite the right side as (y - 5)² - 3. Simplify the left side to get (x - 5)² = (y - 5)² - 3. Therefore, x² = 4a(y - 5).
c) y = x² - 6x + 4:
Complete the square to obtain y² = 4ax form: y² + 6y = x² + 4. Rewrite the right side as (x - 3)² - 5. Simplify the left side to get (y + 3)² = (x - 3)² - 5. Therefore, y² = 4a(x - 3).
d) x = y² + 2y - 1:
Complete the square to obtain x² = 4ay form: x² - 2x = y² - 1. Rewrite the right side as (y + 1)² - 2. Simplify the left side to get (x - 1)² = (y + 1)² - 2. Therefore, x² = 4a(y + 1).