Which functions graph is a translation of the graph of f(x)= 3x^2 + 4 seven units down?

Mathematics

1 answer:

asambeis [7]3 years ago

4 0

Answer:

Option C

Step-by-step explanation:

Consider the function f ( x ) = 3x^2 + 4;

$f ( x ) = 3x^2 + 4,\\\\4 = vertex ( y - intercept ),\\\\\\$

Now if this graph were to be translated 7 units down, considering the function was f ( x ) = 3x^2, the new graph would be f ( x ) = 3x^2 - 7. The same concept is applied to the graph f ( x ) = 3x^2 + 4;

$4 - 7 = - 3,\\f ( x ) = 3x^2 - 3\\\\Solution - Option C$

* Note that a translation doesn't effect the rate with which the graph changes, it only effect's it's position on the coordinate plane

<em>Hope that helps!</em>

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a street light is at the top of a 18 ft tall pole. a woman 6 ft tall walks away from the pole with a speed of 4 ft/sec along a s

shutvik [7]

The most appropriate choice for similarity of triangles will be given by -

Speed of tip of the shadow of woman = 6 ft/s

What are similar triangles?

Two triangles are said to be similar, if the corrosponding angles of the triangles are same and the corrosponding sides of the triangles are in the same ratio.

Here,

The diagram has been attached here

Let the distance of woman from the pole be x ft and the distance of tip of the shadow to the pole be y ft.

Height of street light = 18 ft

Height of woman = 6ft

The two triangles are similar [As height of woman is parallel to the height of pole]

$\frac{y - x}{6}=\frac{y}{18}\\18y - 18x = 6y\\18y - 6y = 18x\\12y = 18x\\y = \frac{18}{12}x\\y = \frac{3}{2}x\\$