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@oliver69
\[f(x)=-x^2-10x\] is a quadratic function with a negative a-coefficient. Hence, its graph is ∩ shaped parabola. 1) Translation of a graph by 5 units downward is a subtraction of 5 from f(x). So we have \[-x^2-10x-5\] 2) A vertical stretch by a factor of 6 is multiplication by positive 6. Hence, \[6(-x^2-10x-5)=-6x^2-60x-30\] 3)Since parabola is symmetrical relevant to the y-axis, we consider a reflection in the x-axis of the graph, which is just multiplication by -1. Hence, \[g(x)=6x^2+60x+30\] (I hope this helps. Good luck on your assignment or whatever.)
thank u
@oliver69 wrote:
\[f(x)=-x^2-10x\] is a quadratic function with a negative a-coefficient. Hence, its graph is ∩ shaped parabola.
1) Translation of a graph by 5 units downward is a subtraction of 5 from f(x). So we have \[-x^2-10x-5\]
2) A vertical stretch by a factor of 6 is multiplication by positive 6. Hence, \[6(-x^2-10x-5)=-6x^2-60x-30\]
3)Since parabola is symmetrical relevant to the y-axis, we consider a reflection in the x-axis of the graph, which is just multiplication by -1. Hence, \[g(x)=6x^2+60x+30\]
(I hope this helps. Good luck on your assignment or whatever.)
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