Question

How to convert 4x² - 1 to vertex form?

a) 4(x - 1)²
b) 4(x + 1)²
c) 4(x - 1)² - 1
d) 4(x + 1)² - 1

Answer 1

To convert 4x² - 1 to vertex form, follow the steps of completing the square by factoring out the common coefficient, adding and subtracting the square of half the coefficient of x, simplifying inside the parentheses, and factoring the squared term as a perfect square.

Step-by-step explanation:

To convert the expression 4x² - 1 to vertex form, we can use the method of completing the square. Here's the step-by-step process:

1. Factor out the common coefficient: 4(x² - 1/4)
2. Complete the square by adding and subtracting the square of half the coefficient of x: 4(x² - 1/4) + 1 - 1
3. Simplify inside the parentheses: 4(x² - 1/4) + 1 - 4/4
4. Factor inside the parentheses as a perfect square: 4(x - 1/2)² - 3/4

Therefore, the expression 4x² - 1 in vertex form is: 4(x - 1/2)² - 3/4.