Write the quadratic function in Standard Form: f(x)=a(x-h)^2+k

Question

Write the quadratic function in standard form.

f(x) = x² − 14x + 54

and

Write the quadratic function in standard form.

f(x) = x² − 6x

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Answer 1

f(x) = x² − 14x + 54

Let a = 1, b = -14, and c = 54.

x = -b/2a = -(-14)/2(1) = 14/2 = 7

f(7) = (7)² - 14(7) + 54 = 49 - 98 + 54 = 5

f(x) = (x - 7)² + 5

f(x) = x² − 6x

Let a = 1, b = -6, and c = 0.

x = -(-6)/2(1) = 6/2 = 3

f(3) = (3)² - 6(3) = 9 - 18 = -9

f(x) = (x - 3)² - 9