Graph f(x) =-2x^+16x-30 by factoring to find the solutions, then find the coordinates of the vertex, and the axis of symmetry. identity the equation for the axis of symmetry, write the solutions and the coordinates of the vertex as ordered pairs. show as much work as possible for full credit. all work should be done by hand.

Observe attached image

Function zeros:

(3, 0), (5, 0)

Vertex:

(4, 2)

Axis of symmetry:

Step-by-step explanation:

First factorize the function

Take -2 as a common factor.

Now factor the expression

You must find two numbers that when you add them, obtain the result -8 and multiplying those numbers results in 15.

These numbers are -5 and -3

Then we can factor the expression in the following way:

The quadratic function cuts the x-axis at x = 3 and at x = 5.

Now we find the coordinates of the vertex.

For a function of the form the x coordinate of its vertex is:

In the function

Then the vertice is:

The y coordinate of the symmetry axis is

The axis of symmetry is a vertical line that cuts the parabola in two equal halves. This axis of symmetry always passes through the vertex.

Then the axis of symmetry is the line

The solutions and the vertice written as ordered pairs are:

Function zeros:

(3, 0), (5, 0)

Vertex:

(4, 2)

the answer is 3/5

step-by-step explanation:

first divide 24 divided by 8 because that is the least common multiple

then divide 40 by 8

then you will get 3/5.

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204