Question

Write the quadratic function 5x2 - 40x + 60 in its vertex form by completing the square. Then

identify its turning point.

Answer 1

There’s no turning point bc the multiplicity is one

Answer 2

9514 1404 393

Answer:

• 5(x -4)² -20
• turning point = (4, -20)

Explanation:

It can work well to factor the leading coefficient from the x-terms.

5(x² -8x) +60

Now, add the square of half the x-coefficient inside parentheses, and subtract the same amount outside parentheses.

5(x² -8x +16) +60 -(5)(16)

5(x -4)² -20 . . . . write as a square, simplify the added constant

The vertex form is ...

5(x -4)² -20

It shows you the vertex is (4, -20). This is the turning point.

_____

Vertex form is a(x -h)² +k, where (h, k) is the vertex.