Respuesta :
The vertex-form of the equation of a parabola is [tex]y=a(x-h)^2+k[/tex],
where (h, k) is the vertex point.
We are given that 9 is the maximum point, and that the axis of symmetry is the line x=-5.
The axis of symmetry passes through the vertex, so the x-coordinate of the vertex is -5. The maximum height is 9 means that the y-coordinate of the vertex is 9.
So: (h, k)=(-5, 9).
Substituting in the vertex-form, now we have:
[tex]y=a(x+5)^2+9[/tex].
We also know that (-7, 1) is a point of the parabola, so this point is an (x, y) which satisfies the equation. That is:
[tex]y=a(x+5)^2+9\\\\1=a(-7+5)^2+9\\\\a(-2)^2=-8\\\\4a=-8\\\\a=-2.[/tex]
Now we have all the constants h, k and a, so we are able to write the equation:
[tex]y=-2(x+5)^2+9[/tex].
Answer: [tex]y=-2(x+5)^2+9[/tex].
where (h, k) is the vertex point.
We are given that 9 is the maximum point, and that the axis of symmetry is the line x=-5.
The axis of symmetry passes through the vertex, so the x-coordinate of the vertex is -5. The maximum height is 9 means that the y-coordinate of the vertex is 9.
So: (h, k)=(-5, 9).
Substituting in the vertex-form, now we have:
[tex]y=a(x+5)^2+9[/tex].
We also know that (-7, 1) is a point of the parabola, so this point is an (x, y) which satisfies the equation. That is:
[tex]y=a(x+5)^2+9\\\\1=a(-7+5)^2+9\\\\a(-2)^2=-8\\\\4a=-8\\\\a=-2.[/tex]
Now we have all the constants h, k and a, so we are able to write the equation:
[tex]y=-2(x+5)^2+9[/tex].
Answer: [tex]y=-2(x+5)^2+9[/tex].
