Question

Convert each equation from the vertex form to the general form.

Answer 1

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`