Solve for x: x²−9=5(x−3).
1 answer:
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Answer is in the pic above. Theorems used:
Exterior angle theorem
Inscribed angle theorem.
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
The first step of completing the square is writing the expression
We have the first two terms exactly the same with the function we start with:
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
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