X^2 - 5x - 20 why is

Question

Complete the Square NOT working in Vertex Form? 

 

 

Answer 1

The expression is x² - 5x - 20.

Since x² - 5x - 20 is not an equation, we can't assume that x² - 5x = 20.

Standard form of parabola y  = ax ² + bx + c

Vertex form of parabola is y  = a (x - h ) ² + k, with vertex (h, k).

The equation of the parabolais y = x² - 5x - 20.

 To convert to vertex form add and subtract (half the x coefficient)² to the expression x² - 5x - 20.

 Here x coefficient = - 5. so, (half the x coefficient)² = (- 5/2)²= 25/4.

Add and subtract 25/4 to the expression.

y = x² - 5x + 25/4 - 20 - 25/4

= (x - 5/2)²- (20 + 25/4)

= (x - 5/2)²- [ (20*4 + 25)/4 ]

= (x - 5/2)²- [ (80 + 25)/4 ]

y = (x - 5/2)²- (105/4).

Compare the above equation with vertex form of parabola y  = a (x - h ) ² + k.

Vertex is (5/2, - 105/4).