## Enter the Quadratic Function in Vertex Form

The quadratic function can be written in many different forms. In this case, we are looking for the vertex form. The vertex form of a quadratic is: f(x)=a(x-h)^2+k Where (h,k) is the vertex.

### Enter the function in the box

To enter the quadratic function in vertex form, input the function in the format “f(x) = a(x – h)^2 + k” where “a” is the coefficient of x^2, “h” is the x-coordinate of the vertex, and “k” is the y-coordinate of the vertex.

### Determine the value of a

In order to determine the value of a for the given function, f(x), we must first identify the vertex of the function. The equation for a quadratic function in vertex form is:

f(x) = a(x – h)^2 + k

where (h, k) is the coordinates of the vertex. To find the vertex, we set the derivative of the function equal to 0 and solve for x. The derivative of the quadratic function is:

f'(x) = 2a(x – h)

Setting this equal to 0 and solving for x gives us:

x = h

So, plugging in h for x in our original equation gives us:

f(h) = a(h – h)^2 + k

f(h) = ah^2 + k

f(h) = a(0)^2 + k

f(h) = ak + k

f(h) = a*k + k*1 (since anything raised to 0 is 1, k*1 can be simplified to just k)

### Determine the value of b

In order to determine the value of b, we need to use the fact that the vertex is at (-b/2a, f(b/2a)). Plugging in our values, we get:

(-b/2*8, f(b/2*8))

(-b/16, f(b/16))

This means that b/16 = -8 and b = -128.

### Determine the value of c

Given the equation f(x) = x^2 + 8x + 13, we can determine the value of c by using the vertex form of the equation. In the vertex form, the equation is written as f(x) = a(x-h)^2 + k, where h and k are the coordinates of the vertex. Therefore, we can set h = -b/(2a) and k = f(-b/(2a)) to solve for c. In our equation, we have a = 1, b = 8, and f(-b/(2a)) = 13. Therefore, c = 13-8(-4) = 29.

## Simplify the Quadratic Function

The quadratic function can be simplified by factoring. In this case, the quadratic function can be factored into (x + 4)(x + 3). This will give you the vertex form of the quadratic function, which is (x + 4)(x + 3).

### Factor the quadratic function

enter the quadratic function in vertex form in the box

In order to factor the quadratic function, we need to find the two numbers that multiply together to give us 8x, and add up to 13. These two numbers are -1 and -13. So, our factored quadratic function is:

f(x) = (x + 1)(x – 13)

### Simplify the function

The quadratic function can be simplified by using the factoring method. First, we need to find the factors of 8x and 13. These are 1 and 8, 1 and 13, and 2 and 4. We can then use these factors to simplify the function as follows:

fxx2 8x 13

fxx2 8x 1 8x 1 13 2 4

fxx8x1 x4 x2 x4 x21

As you can see, the quadratic function can be simplified by using the factoring method. This is a very powerful technique that can be used to simplify many different functions.

## Determine the Quadratic Function’s Vertex

In order to determine the quadratic function’s vertex, you must first take the given equation and rewrite it in standard form. This can be done by completing the square. You will then need to take the derivative of this function in order to find the x-coordinate of the vertex.

### Find the x-coordinate of the vertex

The x-coordinate of the vertex can be found using the formula x=-b/2a.

In the Quadratic function fxx2 8x 13, a=1, b=8, and c=13.

Therefore, the x-coordinate of the vertex is: x=-8/2(1)=-4.

### Find the y-coordinate of the vertex

To find the y-coordinate of the vertex, plug the x-coordinate of the vertex (h) into the equation for y:

y = f(x) = a(x-h)^2 + k

y = f(h) = a(h-h)^2 + k

y = f(h) = ah^2 – 2ah + h + k

y = ah^2 – 2ah + h + k

## Graph the Quadratic Function

You can graph the quadratic function by finding the equation’s vertex. The vertex is the highest or lowest point on the graph of the equation. To find the vertex, start by solving the equation for x. Then, plug your answer back into the equation to solve for y. These coordinates are the x and y values of the vertex.

### Plot the points on the graph

In order to graph the quadratic function, you will first need to find the vertex. To do this, you will need to use the Quadratic Formula, which is:

x = -b/2a

Plugging in the values from the given equation, you will get:

x = -8/2(13)

x = -8/26

x = -1/3

The y-coordinate of the vertex can be found by plugging in the x-coordinate of the vertex into the equation. In this case, it would be:

y = (13)(-1/3)^2 + 8(-1/3) + 13

y = 169/27 + 8(-1/3) + 13

y = 169/27 – 8/27 + 13 // since (-1/3)(8) is -8/27 and not 8/-27 as some might think!

y = 180/27 + 13 // simplify 169/27 + 8/-27 becomes 169/27 – 8/27 which is just 160/27

### Connect the points to form the graph of the quadratic function

In order to graph the quadratic function, you will need to connect the points. You can do this by using a pencil and paper or by using a graphing calculator.

If you are using a graphing calculator, you will need to input the quadratic function in vertex form in the box. Once you have done this, you will be able to see the points on the graph. You can then connect the points to form the graph of the quadratic function.

If you are using a pencil and paper, you will need to plot the points on the graph. You can then connect the points to form the graph of the quadratic function.