Respuesta :
the vertex is either the maximum or minimum value
since the leading coefinet is negative (the number in front of the x² term), the parabola opens down and is a maximum
so
A.
a hack version is to use the -b/(2a) form
if you have f(x)=ax²+bx+c, then the x value of the vertex is -b/(2a)
so
given
f(x)=-1x²+16x-60
the x value of the vertex is -16/(2*-1)=-16/-2=8
the y value is f(8)=-1(8)²+16(8)-60=
-1(64)+128-60=
4
the vertex is (8,4)
so you selll 8 candels to make the max profit which is $4
B.
x intercepts are where the line crosses the x axis or where f(x)=0
solve
0=-x²+16x-60
0=-1(x²-16x+60)
factor
what 2 numbers multiply to get 60 and add to get -16
-6 and -10
0=-1(x-6)(x-10)
set each factor to 0
0=x-6
x=6
0=x-10
10=x
x intercepts are at x=6 and 10
that is where you make 0 profit
since the leading coefinet is negative (the number in front of the x² term), the parabola opens down and is a maximum
so
A.
a hack version is to use the -b/(2a) form
if you have f(x)=ax²+bx+c, then the x value of the vertex is -b/(2a)
so
given
f(x)=-1x²+16x-60
the x value of the vertex is -16/(2*-1)=-16/-2=8
the y value is f(8)=-1(8)²+16(8)-60=
-1(64)+128-60=
4
the vertex is (8,4)
so you selll 8 candels to make the max profit which is $4
B.
x intercepts are where the line crosses the x axis or where f(x)=0
solve
0=-x²+16x-60
0=-1(x²-16x+60)
factor
what 2 numbers multiply to get 60 and add to get -16
-6 and -10
0=-1(x-6)(x-10)
set each factor to 0
0=x-6
x=6
0=x-10
10=x
x intercepts are at x=6 and 10
that is where you make 0 profit
The vertex an it's meaning in the context of the problem are; (8,4) which means you selll 8 candels to make a maximum profit of $4
What is the vertex point of the equation?
The vertex of a parabola could either be the maximum or minimum value.
The equation of the function is;
f(x) = -x² + 16x - 60
The leading coefficient is negative and it means that the parabola opens downward and is a maximum.
A)The vertex of the parabola is at; x = -b/(2a)
Since our equation is f(x) = -x² + 16x - 60, then;
x-value of the vertex is;
x = -16/(2 * -1)
x = 8
y-value of vertex is;
f(8) = -1(8)² + 16(8) - 60 = 4
Coordinates of the vertex is (8,4) which means you selll 8 candels to make a maximum profit of $4
B) x-intercepts are where f(x)=0. Thus;
-x² + 16x - 60 = 0
(x² - 16x + 60)
Using quadratic equation solver, we have;
x intercepts are at x = 6 and 10
This means no profit is made at when x = 6 and 10
Read more about Vertex Point at; https://brainly.com/question/17987697
