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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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