What is the y-value of the vertex of the function f(x) = –(x – 3)(x + 11)?

Answers

49

Step-by-step explanation:

The given function is f(x)=-(x-3)(x+11).

We expand to get:

f(x)=-x^2-8x+33

We complete the square to obtain the vertex form as follows:

f(x)=-(x^2+8x)+33

f(x)=-(x^2+8x+16)--16+33

f(x)=-(x^2+8x+16)+16+33

f(x)=-(x+4)^2+49

This function is now of the form:

f(x)=a(x-h)+k, where (h,k)=(-4,49) is the vertex.

The y-value of the vertex is therefore 49

49

Step-by-step explanation:

Given

f(x) = - (x - 3)(x + 11)

Find the zeros by setting f(x) = 0, that is

- (x - 3)(x + 11) = 0

Equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x + 11 = 0 ⇒ x = - 11

The vertex lies on the axis of symmetry which is situated at the midpoint of the zeros

x_{vertex} = \frac{3-11}{2} = \frac{-8}{2} = - 4

Substitute x = - 4 into f(x) for y- coordinate of vertex

f(- 4) = -(- 7)(7) = 49 ← y- value of vertex

49

Step-by-step explanation:

f(x)=-(x-3)(x+11)

The zeros of the equation are 3 and -11

The vertex is  1/2 way between the two values

(3+-11)/2 = -8/2 = -4

The vertex is at x= -4

We substitute this value into the equation to find the y value

f(x)=-(-4-3)(-4+11)

    = -(-7)(7)

    =49

49.

Step-by-step explanation:

We have been a function f(x)=-(x-3)(x+11). We are asked to find the y-value of vertex of the given function.  

Upon multiplying both factors, we will get,

f(x)=-(x*x+11*x-3*x-3*11)

f(x)=-(x^2+11x-3x-33)

f(x)=-(x^2+8x-33)

f(x)=-x^2-8x+33        

Now, we  will use \frac{-b}{2a} formula to find the x-coordinate of vertex of parabola.

\frac{--8}{2*-1}

\frac{8}{-2}

-4

Since the x-coordinate of vertex of parabola is -4, so we will substitute x=-4 in our equation to find y-coordinate of parabola.

f(-4)=-(-4)^2-8(-4)+33  

f(-4)=-16+32+33  

f(-4)=49  

Therefore, the y-coordinate of vertex of the given parabola is 49.

49 just took the unit review

Step-by-step explanation:

( −4;49)

is the answer


What is the y-value of the vertex of the function f(x)=-(x-3)(x+11)? a.-8b.-4 c.33 d.49​

y- value of the vertex for the given function \:f\left(x\right)\:=\:-\left(x\:-\:3\right)\left(x\:+\:11\right) is 49.

Step-by-step explanation:

Given : The function \:f\left(x\right)\:=\:-\left(x\:-\:3\right)\left(x\:+\:11\right)

We have to find the y- value of the vertex for the given function.

Consider the given function  \:f\left(x\right)\:=\:-\left(x\:-\:3\right)\left(x\:+\:11\right)

The vertex of the up-down facing parabola of the form y=a\left(x-m\right)\left(x-n\right) is the average of the zeros, x_v=\frac{m+n}{2}

Thus, here, m = 3 , n = -11 and a = 1

x_v=\frac{3+\left(-11\right)}{2}=-4

Thus, x- value of vertex is -4.

Now, put x = -4 to get y values

y_v=-\left(-4-3\right)\left(-4+11\right)=49

Thus, y- value of the vertex for the given function \:f\left(x\right)\:=\:-\left(x\:-\:3\right)\left(x\:+\:11\right) is 49.

y- value of the vertex for the given function \:f\left(x\right)\:=\:-\left(x\:-\:3\right)\left(x\:+\:11\right) is 49.

Step-by-step explanation:

Given : The function \:f\left(x\right)\:=\:-\left(x\:-\:3\right)\left(x\:+\:11\right)

We have to find the y- value of the vertex for the given function.

Consider the given function  \:f\left(x\right)\:=\:-\left(x\:-\:3\right)\left(x\:+\:11\right)

The vertex of the up-down facing parabola of the form y=a\left(x-m\right)\left(x-n\right) is the average of the zeros, x_v=\frac{m+n}{2}

Thus, here, m = 3 , n = -11 and a = 1

x_v=\frac{3+\left(-11\right)}{2}=-4

Thus, x- value of vertex is -4.

Now, put x = -4 to get y values

y_v=-\left(-4-3\right)\left(-4+11\right)=49

Thus, y- value of the vertex for the given function \:f\left(x\right)\:=\:-\left(x\:-\:3\right)\left(x\:+\:11\right) is 49.

The y-value of the vertex is 49
The y-value of the vertex is 49


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