A^2+b^2=c^2
Is the Pythagorean theorem
Answer: Option C
Step-by-step explanation:
Given the quadratic equation
, substitute
:

In this case, to find the solutions of the given quadratic equation, you must factor out the variable "x". Then:

Therefore, you get that the solutions of this equation are the following:

Then, the answer is:
This matches with the option C.
Part A:

The first step of completing the square is writing the expression

as

which expands to

.
We have the first two terms exactly the same with the function we start with:

and

but we need to add/subtract from the last term, 49, to obtain 41.
So the second step is to subtract -8 from the expression

The function in completing the square form is

Part B:
The vertex is obtained by equating the expression in the bracket from part A to zero


It means the curve has a turning point at x = -7
This vertex is a minimum since the function will make a U-shape.
A quadratic function

can either make U-shape or ∩-shape depends on the value of the constant

that goes with

. When

is (+), the curve is U-shape. When

(-), the curve is ∩-shape
Part C:
The symmetry line of the curve will pass through the vertex, hence the symmetry line is

This function is shown in the diagram below