Question

Is this standard form for the parabola x^2=y+8x=16?

Answer 1

\[x ^{2}=y+8x-16\]
\[(x-4)^{2}=(y-16)\]

Answer 2

@ganeshie8

Answer 3

or\[(x-0)^{2}=4(2)(y-16)\]

Answer 4

@zepdrix

Answer 5

@dan815 @aajugdar

Answer 6

y=ax^2+bx+c is standard form right?

Answer 7

for a parabola standard form is (y-k)^2=4p(x-h) or (x-h)^2=4p(y-k)

Answer 8

The general equation of a parabola is:
\[y ^{2}=4ax\ ...........(1) \]
The equation that you posted
(y-k)^2=4p(x-h)
is the curve (1) given a translation of
\[\left(\begin{matrix}h \\ k\end{matrix}\right)\]

Answer 9

but thats what the textbook wants me to use to create an equation-standard form equation of the parabola

Answer 10

Please post the exact question from the textbook.

Answer 11

Identify the conic section represented by each equation. Write the equation in standard form and graph the equation.
\[x ^{2}=y+8x-16\]

Answer 12

If the curve of the parabola
\[y ^{2}=4ax\]
is reflected in the line y = x we get the graph of the inverse curve which is:
\[y=\frac{1}{4a}x ^{2}\]

Answer 13

The given equation is
\[x ^{2}=y+8x-16\]
Rearranging gives
\[y=x ^{2}-8x+16\]
which factorizes to
\[y=(x-4)^{2}\ .............(2)\]
(2) is the equation of a parabola with vertex (4, 0 and translation
\[\left(\begin{matrix}4 \\ 0\end{matrix}\right)\]
When x = 0, y = 16 and when y = 0, x = 4.
The sketch of the curve follows: