SOLUTION: Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function f(x)=-2x^2+2x+9. The x coordinate of the vertex is? (Type a simplified fraction) The

Question 157345: Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function f(x)=-2x^2+2x+9.
The x coordinate of the vertex is? (Type a simplified fraction)
The y coordinate of the vertex is? (Type a simplified fraction)
The equation of the line of symmetry is x=?
The maximum or minimum of f(x) is?
The value of f(x)=19/2 is maximum or minimum?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

In order to find the vertex, we first need to find the x-coordinate of the vertex.

To find the x-coordinate of the vertex, use this formula: .

Start with the given formula.

From , we can see that , , and .

Plug in and .

Multiply 2 and to get .

Reduce.

So the x-coordinate of the vertex is . Note: this means that the axis of symmetry is also .

Now that we know the x-coordinate of the vertex, we can use it to find the y-coordinate of the vertex.

Start with the given equation.

Plug in .

Square to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

So the y-coordinate of the vertex is .

So the vertex is

.

Also, since the leading coefficient is negative, this means that the vertex is at a maximum.

----------------------------------------------------

So using this info we can answer the following:

The x coordinate of the vertex is

The y coordinate of the vertex is

The equation of the line of symmetry is

The maximum or minimum of f(x) is

The value of f(x)=19/2 is a maximum
RELATED QUESTIONS
Find the vertex,the line of symmetry, the maximum or minimum value of the quadratic... (answered by Fombitz)

Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic... (answered by ewatrrr)

Find the vertex the line of symmetry, the maximum or minimum value of the quadratic... (answered by oberobic)

Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic... (answered by lwsshak3)

Find the vertex line of symmetry maximum or minimum value graph the function... (answered by lwsshak3)

Find the vertex, line of symmetry, the maximum or minimum value of the quadratic... (answered by Alan3354)

Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic... (answered by Mathtut)

Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic... (answered by solver91311)

Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic... (answered by Fombitz)

Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic... (answered by ewatrrr)