Question

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

Question 4 options:

a = -5, opens down


a = -5, opens up


a = 7, opens up


a = 7, opens down

Answer 1

Answer:
a = -5, opens down

Step-by-step explanation:
The general form of the quadratic equation is:
f(x) = a(x-h)² + k where (h,k) is the vertex of the parabola.

The value of the "a" determines whether the parabola is open upwards or downwards:
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

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

The attached image shows the graph of the given function

Hope this helps :)

Answer 2

we know that
the equation of the vertical parabola in the vertex form is
y=a(x-h)²+k
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+6
a=-5
so
a< 0 -------> the parabola open downwards

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

the answer is the option
a = -5, opens down

see the attached figure