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stepladder [879]
2 years ago
9

NO LINKS!!! Find the equation of the PARABOLA with a vertex at (-2, 6) and passing through the point (1, -3)​

Mathematics
2 answers:
levacccp [35]2 years ago
7 0

General equation of parabola

  • y=a(x-h)²+k

for vertex(h,k)

Now

\\ \rm\Rrightarrow y=a(x+2)^2+6

  • Put (1,-3) and find a

\\ \rm\Rrightarrow -3=a(1+2)^2+6

\\ \rm\Rrightarrow -9=a(3)^2

\\ \rm\Rrightarrow -9=9a

\\ \rm\Rrightarrow a=-1

So

equation of parabola

\\ \rm\Rrightarrow y=-(x+2)^2+6

Mrac [35]2 years ago
4 0

Answer:

y=-(x+2)^2+6

Step-by-step explanation:

<u>Vertex form of a quadratic equation</u>

y=a(x-h)^2+k

where:

  • (h, k) is the vertex
  • a is some constant

Given:

  • vertex = (-2, 6)
  • point on parabola = (1, -3)

Substitute the given values into the vertex equation and solve for a:

\implies -3=a(1-(-2)^2+6

\implies -3=a(3)^2+6

\implies -3=9a+6

\implies 9a=-9

\implies a=-1

<u>Vertex form</u>

Substitute the given vertex and the found value of a into the vertex equation:

\implies y=-(x+2)^2+6

<u>Standard form</u>

Expand the brackets of the vertex form:

\implies y=-(x^2+4x+4)+6

\implies y=-x^2-4x+2

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