Question

Convert the following Quadratic Equations from Vertex Form to Standard Form.

Answer 1

4)

Given:

The vertex form is given as,

`y=-(1)/(3)(x+6)^2-1`

The objective is to convert the vertex form to standard form.

The standard form can be obtained as,

`\begin{gathered} y=-(1)/(3)(x+6)^2-1 \\ =-(1)/(3)(x^2+6^2+2(x)(6))-1 \\ =-(1)/(3)(x^2+36+12x)-1 \\ =-(x^2)/(3)-(36)/(3)+(12x)/(3)-1 \\ =-(x^2)/(3)-12+4x-1 \\ =-(x^2)/(3)+4x-13 \end{gathered}`

Here,

`\begin{gathered} a=-(1)/(3) \\ b=4 \\ c=-13 \end{gathered}`

Hence, the required standard form of the equation is obtained.