130k views
3 votes
Convert each equation from the vertex form to the general form.

Convert each equation from the vertex form to the general form.-example-1
User Sewake
by
8.7k points

1 Answer

5 votes

The standard form is:


y=ax^2+bx+c

To get it from the vertex form we need to do the operations and simplify like terms. With this in mind we have:

a.


\begin{gathered} y=(x+5)^2+4 \\ y=x^2+10x+25+4 \\ y=x^2+10x+29 \end{gathered}

Therefore the standard form is:


y=x^2+10x+29

b.


\begin{gathered} y=2(x-7)^2-8 \\ y=2(x^2-14x+49)-8 \\ y=2x^2-28x+98-8 \\ y=2x^2-28x+90 \end{gathered}

Therefore the standard form is:


y=2x^2-28x+90

c.


\begin{gathered} y=-3(x+4)^2+1 \\ y=-3(x^2+8x+16)+1 \\ y=-3x^2-24x-48+1 \\ y=-3x^2-24x-47 \end{gathered}

Therefore the standard form is:


y=-3x^2-24x-47

d.


\begin{gathered} y=0.5(x-3)^2-4.5 \\ y=0.5(x^2-6x+9)-4.5 \\ y=0.5x^2-3x+4.5-4.5 \\ y=0.5x^2-3x \end{gathered}

Therefore the standard form is:


y=0.5x^2-3x

User Kate
by
7.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories