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Charra [1.4K]
3 years ago
5

What are the coordinates of the vertex for f(x) = 2x2 + 4x + 9?

Mathematics
2 answers:
Blizzard [7]3 years ago
8 0
Vertex: (-1,7)
Focus: (-1, 57 over 8)
Axis of Symmetry(AOS): x=-1
Directories: y= 55 over 8
X , Y
-3 , 15
-2 , 9
-1 , 7
0 , 9
1 , 5
Vlada [557]3 years ago
5 0
Your equation f(x)=2x^2+4x+9 is in the form y=ax^2+bx+c
The vertex only relies on "a" and "b" though, so that +9 doesn't really matter in this case.  The vertex of a parabola is located where 
x=\frac{-b}{2a}=\frac{-4}{2(2)}=-1
So your x-coordinate is -1.  You need to find f(-1) to find your y-coordinate, and then you list it in the form (-1, y).
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Answer:

7) 28.8 in

8) 80.6 mm

9) 68.3 cm

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Applying Pythagoras' Theorem,

x²= 16² +24²

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x² +40²= 90²

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9) See the attached picture for better understanding.

1st picture shows the simplified diagram of the question, indicating where line x lies in the rectangular prism.

Now, if we cut the prism into half diagonally so that we obtain 2 equal triangular prism, we would obtain 2 prisms that look like the one drawn in picture 2.

Now zoom in to the blue face of the prism, we would get a triangle as shown in picture 3.

Let's find the value of y.

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y²= 40² +54²

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y= √4516

Look at picture 2 again at focus at the pink shaded triangle. It has been re-drawn in picture 4.

Now we know that y= √4516.

Applying Pythagoras' Theorem,

x²= (√4515)² +12²

x²= 4660

x= √4660

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Answer:

the answer is B

Step-by-step explanation:

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