Respuesta :

Answer:

=> the passing point's y cord is lower than vertex, meaning it is a reflection
[tex]y=-a\left(x+h\right)^{2}-k[/tex]

=>Apply the vertex to hk form
[tex]y=-a\left(x+4\right)^{2}-1[/tex]
=> Find a by plugging X and Y of the passing through point

[tex]-3=-a\left(-2+4\right)^2-1[/tex]

=> solve
[tex]-4a-1+1=-3+1[/tex]

[tex]a=\frac{1}{2}[/tex]

Therefore the equation for this is,

[tex]y=-\frac{1}{2}\left(x+4\right)^{2}-1[/tex]

Ver imagen Аноним
semsee45

Answer:

[tex]y=-\dfrac{1}{2}(x+4)^2-1[/tex]

Step-by-step explanation:

Vertex form:  [tex]y=a(x-h)^2+k[/tex]  

where:

  • [tex](h, k)[/tex] is the vertex
  • [tex]a[/tex] is some constant

Given:

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

Substitute given values into the formula to find [tex]a[/tex]:

[tex]\implies -3=a((-2)-(-4))^2+(-1)[/tex]

[tex]\implies -3=a(2)^2-1[/tex]

[tex]\implies -3=4a-1[/tex]

[tex]\implies -2=4a[/tex]

[tex]\implies a=-\dfrac{2}{4}=-\dfrac{1}{2}[/tex]

Therefore, the equation of the parabola is:

[tex]y=-\dfrac{1}{2}(x+4)^2-1[/tex]

Ver imagen semsee45

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