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Question

Express f(x) = x^2-6x+14 in the form f(x) = (x-h)^2+k, where h and k are to be determined. 

Write down the coordinates of the vertex of the parabola with equation 
y = x^2-6x+14? 

Answer 1

The function is f(x) = x² - 6x + 14.

Consider y = x² - 6x + 14

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

y = x² - 6x + 14

To change the expression into a perfect square, add (half the x coefficient)² to each side of the expression.

x  coefficient = - 6

then (half the x coefficient)² is (- 6/2)² = 9.

Add 9 to each side.

y + 9 = 1(x² - 6x) + 14 + 9

y + 9 = 1((x² - 6x + 9) + 14

y + 9 = (x - 3)² +14

Subtract 9 from each side.

y = (x - 3)² +14 - 9

y = (x - 3)² + 5

The above equation is in the vertex form of parabola y = a(x - h)² + k.

Vertex of parabola (h,k) is (3,5)

Therefore,

The equation of parabola in vertex form is y = (x - 3)² + 5.

Vertex (3,5).