The equation of a parabola is of the form [tex]y = a(x - h)^2+ k[/tex]
The equation of the parabola is: [tex]y = -6(x + 5)^2 + 9[/tex]
The given parameters are:
[tex](h,k) = (-5,9)[/tex] --- the vertex
[tex](x,y) = (-7,-15)[/tex]
Substitute [tex](h,k) = (-5,9)[/tex] in [tex]y = a(x - h)^2+ k[/tex]
[tex]y = a(x --5)^2 + 9[/tex]
[tex]y = a(x +5)^2 + 9[/tex]
Substitute [tex](x,y) = (-7,-15)[/tex]
[tex]-15 = a(-7 +5)^2 + 9[/tex]
[tex]-15 = a(-2)^2 + 9[/tex]
Collect like terms
[tex]-9-15 = a(-2)^2[/tex]
[tex]-24 = a(-2)^2[/tex]
[tex]-24 = 4a[/tex]
Divide both sides by 4
[tex]-6 = a[/tex]
Rewrite as:
[tex]a = -6[/tex]
Substitute [tex]a = -6[/tex] in [tex]y = a(x +5)^2 + 9[/tex]
[tex]y = -6(x + 5)^2 + 9[/tex]
Hence, the equation of the parabola is: [tex]y = -6(x + 5)^2 + 9[/tex]
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