CONVERTIG FROM VERTEX FORM TO STANDARD FORM

To convert standard form to vertex form, we may follow the different ways.

Convert the following quadratics from vertex form to standard form.

Problem 1 :

y = -(x – 1)² – 1

Solution :

y = -(x – 1)² – 1

Using the algebraic identity, we can expand this and then distribute the negative sign.

(x – 1)² = x² - 2x(1) + 1²

(x – 1)² = x² - 2x + 1

y = -(x² - 2x + 1) – 1

Distributing the negative, we get

y = -x² + 2x - 1 – 1

y = -x² + 2x - 2

Problem 2 :

y = 2(x – 2)² – 3

Solution :

y = 2(x – 2)² – 3

Using the algebraic identity, we can expand it and multiply by 2.

(x – 2)² = x² - 2x(2) + 2²

(x – 2)² = x² - 4x + 4

y = 2(x² - 4x + 4) – 3

Distributing 2, we get

y = 2x² - 8x + 8 – 3

Combining the like terms, we get

y = 2x² - 8x + 5

Problem 3 :

y = (x + 4)² + 4

Solution :

y = (x + 4)² + 4

Using the algebraic identity, we can expand it and multiply by 2.

(x + 4)² = x² - 2x(4) + 4²

(x – 1)² = x² - 8x + 16

y = (x² - 8x + 16) + 4

Combining the like terms, we get

y = x² - 8x + 20

Problem 4 :

y = (1/2)(x - 2)² - 4

Solution :

y = (1/2)(x - 2)² - 4

Using the algebraic identity, we can expand it and multiply by 2.

(x - 2)² = x² - 2x(2) + 2²

(x – 2)² = x² - 4x + 4

y = (1/2)(x² - 4x + 4) - 4

Distributing 1/2, we get

y = (1/2)x² - 2x + 2 - 4

y = (1/2)x² - 2x - 2