Question

F(x)=2^2-5x+10

Graphing ((x) = ax?
+ ox + c
Complete the square to write each function in the form
f(x) = a(x - h)? + k.

Answer 1

Answer: The given function is f(x) = 2x^2 - 5x + 10.

To write this function in the form f(x) = a(x - h)^2 + k, we can complete the square as follows:

f(x) = 2(x^2 - 5/2x) + 10

= 2(x^2 - 5/2x + 25/16 - 25/16) + 10 (adding and subtracting (5/4)^2 inside the parenthesis to complete the square)

= 2((x - 5/4)^2 - 25/16) + 10

= 2(x - 5/4)^2 - 5/2

Therefore, the function f(x) can be written in the form f(x) = 2(x - 5/4)^2 - 5/2.

Note that this form of the function is called the vertex form, where the vertex is at the point (h,k) and the value of a determines the direction and scale of the parabola.