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dimulka [17.4K]
3 years ago
11

What is the a-value of the function, then determine if the graph opening up or down f(x)=−5(x+7)2+6?

Mathematics
2 answers:
Kay [80]3 years ago
6 0
We know that
the equation of the vertical parabola in the vertex form is
<span>y=a(x-h)²+k
</span>where 
(h,k) is the vertex of the parabola
if a> 0 then
 the parabola opens upwards

if a< 0
then the parabola open downwards

in this problem  we have
f(x)=−5(x+7)²<span>+6
</span>a=-5
so
a< 0 -------> the parabola open downwards

the vertex is the point (-7,6) is a maximum

the answer is the option
<span>a = -5, opens down</span> 

see the attached figure

Sergeeva-Olga [200]3 years ago
3 0
<span><u><em>Answer:</em></u>
a = -5, opens down

<u><em>Explanation:</em></u>
<u>The general form of the quadratic equation is:</u>
f(x) = a(x-h)</span>²<span> + k where (h,k) is the vertex of the parabola.

<u>The value of the "a" determines whether the parabola is open upwards or downwards:</u>
1- if the value of "a" is positive, this means that parabola opens upwards
2- if the value of "a" is negative, this means that the parabola opens downwards

<u>Now, for the given:</u>
f(x) = -5(x+7)</span>²<span> + 6
<u>By comparison, we can note that:</u>
a = -5
The value of "a" is <u>negative</u> which means that the parabola opens down.

The attached image shows the graph of the given function

Hope this helps :)</span>

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You are to manufacture a rectangular box with 3 dimensions x, y and z, and volume v=8000. Find the dimensions which minimize the
Inga [223]

Answer:

20 by 20 by 20

Step-by-step explanation:

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x is the length of the box

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S = 2xy+16000/x+16000/y

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Similarly,

dS/dy = 2x  + (-160000y⁻²)

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Note that at the turning point, ds/dx = 0 and ds/dy = 0, hence;

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2y = 16000/x² and 2x = 16000/y²

2y = 16000/(8000/y²)²

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2x = 16000/20²

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x = 20

Since Volume of the box is V = xyz

8000 = 20(20)z

8000 = 400z

z = 8000/400

z = 20

Hence, the dimensions which minimize the surface area of this box is 20 by 20 by 20.

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