Which of the following statements are true about the graph of f(x) = 6(x + 1)2 -9?
Check all of the boxes that apply.

A-The vertex is (1, -9).

B-The graph opens upward.

C-The graph is obtained by shifting the graph of f(x) = 6(x + 1)2 up 9 units.

D-The graph is steeper than the graph of f(x) = x2.

E*The graph is the same as the graph of f(x) = 6x2 + 12x - 3.

B is true The coefficient of x^2 is positive so it opens up.

Its also steeper because of the presence of the 6 x^2 so D is true.

Also if we expand the given form of the equation we obtain option E
So E is true also.

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nishantwork777 nishantwork777 · Answer 2 · 2021-10-06T14:28:18+02:00

Answer:

The correct options are:

B - The graph opens upward
D - The graph is steeper than the graph of [tex]f(x)=x^2[/tex]
E - The graph is same as the graph of [tex]f(x)=6x^2+12x-3[/tex]

Step-by-step explanation:

Given information

The equation of the graph

[tex]f(x)=6(x+1)^2-9[/tex]

For the conclusion we need to plot the graph

As, we can see the coefficient of [tex]x^2[/tex] is positive in the given equation,

So, the graph will open upwards.

Hence, option B is correct.

Also,

The equation has the presence of [tex]6x^2[/tex] which will give grater value of slope then [tex]x^2[/tex],

Hence graph is steeper than the graph of [tex]f(x)=x^2[/tex]

So, The option D is also correct.

Now, simplifying the given equation:

[tex]f(x)=6(x+1)^2-9\\f(x)=6(x^2+2x+1)-9\\f(x)= 6x^2+12+6-9\\f(x)=6x^2+12x-3[/tex]

The above expression is same as the given expression

So, graph of the expression will also be same.

Hence, option E is also correct.

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