Question

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14. Find 5he equation of the parabola with a vertex at (-4,-1) and passing through the point (-2, -3).​

Answer 1

=> the passing point's y cord is lower than vertex, meaning it is a reflection

`y=-a\left(x+h\right)^(2)-k`

=>Apply the vertex to hk form

`y=-a\left(x+4\right)^(2)-1`
=> Find a by plugging X and Y of the passing through point

`-3=-a\left(-2+4\right)^2-1`

=> solve

`-4a-1+1=-3+1`

`a=(1)/(2)`

Therefore the equation for this is,

`y=-(1)/(2)\left(x+4\right)^(2)-1`

Answer 2

`y=-(1)/(2)(x+4)^2-1`

Explanation:

Vertex form:
`y=a(x-h)^2+k`

where:

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

Given:

• vertex = (-4, -1)
• point on parabola = (-2, -3)

Substitute given values into the formula to find
`a`:

`\implies -3=a((-2)-(-4))^2+(-1)`

`\implies -3=a(2)^2-1`

`\implies -3=4a-1`

`\implies -2=4a`

`\implies a=-(2)/(4)=-(1)/(2)`

Therefore, the equation of the parabola is:

`y=-(1)/(2)(x+4)^2-1`