Question

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

Answer 1

4)

Given:

The vertex form is given as,

$y=-\frac{1}{3}(x+6)^2-1$

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

The standard form can be obtained as,

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

Here,

$\begin{gathered} a=-\frac{1}{3} \\ b=4 \\ c=-13 \end{gathered}$

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