Question

The vertex form of the equation of a parabola is y=2 (x+4)^2-21. What is the standard form of the equation?

Answer 1

for a quadratic, is simply the quadratic itself expanded, nothing to it, so we'll just simply expand the binomial and simplify,


`\bf y=2(x+4)^2-2\implies y=2(x^2+8x+16)-2 \\\\\\ y=2x^2+16x+32-2\implies y=2x^2+16x+30`

Answer 2

The standard form of the equation of a parabola is
`y=2x^2+16x+11`

Explanation:

Given : The vertex form of the equation of a parabola is
`y=2(x+4)^2-21`.

To find : What is the standard form of the equation?

Solution :

The standard form of the equation of a parabola is the expansion of the vertex form,

Now, we open the square term of the vertex form and solve it

`y=2(x+4)^2-21`

`y=2(x^2+4^2+2(x)(4))-21`

`y=2(x^2+16+8x)-21`

`y=2x^2+32+16x-21`

`y=2x^2+16x+11`

Therefore, The standard form of the equation of a parabola is
`y=2x^2+16x+11`