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

Answer:

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

Step-by-step 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  $y=2x^2+16x+11$