# Write the quadratic function in the form f(x)= a(x-h)^2+k.

Graphed Vertical parabola with the point (2,1).

## Roots:

X=2 X=1
Sum of the roots= 3
Product of the roots= 2

Always assume a=1.
b is always the opposite sign
1x^2-3x+2=0
a=1 b=-3 c=2

Axis of symmetry=-b/2a
So that’s 3/2(1) which equals 3/2

We plug the axis of symmetry which is going to equal x (or in this case, h) into our quadratic equation to find f(x), which is also y and k.

Y=(3/2)^2-3(3/2)+2
Y= 9/4-9/2+3
Y=3/4
So now we know that k=3/4

1(x-3/2)^2+3/4

## To write the quadratic function in the form f(x) = a(x-h)^2 + k, we can use the given point (2,1) to determine the values of h and k.

First, let's use the point (2,1) to find the value of h. Since the parabola is graphed vertically, the vertex is given by the coordinates (h, k). Therefore, h = 2.

Next, let's find the value of k. Since the parabola passes through the point (2,1), we substitute x = 2 and y = 1 into the function f(x):
1 = a(2 - 2)^2 + k
1 = a(0) + k
1 = k

So, k = 1.

Now we have the values of h and k, which are h = 2 and k = 1, respectively. We can substitute these values into the general form f(x) = a(x - h)^2 + k to get the quadratic function in the desired form:

f(x) = a(x - 2)^2 + 1

## To express a quadratic function in the form f(x) = a(x - h)^2 + k, we need to find the values of a, h, and k.

Given that the graph is a vertical parabola and passes through the point (2, 1), we know that the vertex of the parabola is located at (h, k). Therefore, the vertex-form equation becomes f(x) = a(x - 2)^2 + 1.

To find the value of a, we need more information because the vertex alone cannot determine the value of a. This could be provided in the problem statement or through additional given points. Please provide more information, or if you have any other questions, feel free to ask.