If the equation of a parabola is y = 9(x - 2)2 + v, and its vertex is (2, -4), what is the value of v in the equation?

1 answer:

5 0

If the vertex of the parabola is (h,k) the equation of the parabola will be
y = a(x - h)² + k

From the question (h,k) is (2,-4) then the equation of the parabola will be
y = a(x - 2)² + (-4)

Compare the equation
y = a(x - 2)² + (-4)
with
y = 9(x - 2)² + v
The value of a is 9 and the value of v is (-4).

The answer of the question ⇒ the value of v is (-4)

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Find a nonzero vector orthogonal to the plane through the points: ????=(0,0,1), ????=(−2,3,4), ????=(−2,2,0).

ser-zykov [4K]

Answer:

The nonzero vector orthogonal to the plane is <-9,-8,2>.

Step-by-step explanation:

Consider the given points are P=(0,0,1), Q=(−2,3,4), R=(−2,2,0).

$\overrightarrow {PQ}==$

$\overrightarrow {PR}==$

The nonzero vector orthogonal to the plane through the points P,Q, and R is

$\overrightarrow n=\overrightarrow {PQ}\times \overrightarrow {PR}$

$\overrightarrow n=\det \begin{pmatrix}i&j&k\\ \:\:\:\:\:-2&3&3\\ \:\:\:\:\:-2&2&-1\end{pmatrix}$

Expand along row 1.

$\overrightarrow n=i\det \begin{pmatrix}3&3\\ 2&-1\end{pmatrix}-j\det \begin{pmatrix}-2&3\\ -2&-1\end{pmatrix}+k\det \begin{pmatrix}-2&3\\ -2&2\end{pmatrix}$