Question
find the axis of symmetry of the following quadratic function by completing the square
f(x)=x^2+8x
f(x)=x^2+8x
Answers
GPT 3.5
To find the axis of symmetry of the quadratic function f(x) = x^2 + 8x, we first complete the square.
f(x) = x^2 + 8x
To complete the square, we need to add and subtract (8/2)^2 = 16 to the expression:
f(x) = x^2 + 8x + 16 - 16
f(x) = (x + 4)^2 - 16
Now we have the function in vertex form:
f(x) = (x + 4)^2 - 16
The axis of symmetry for a quadratic function in vertex form y = a(x-h)^2 + k is x = h. Therefore, the axis of symmetry for the function f(x) = (x + 4)^2 - 16 is x = -4.
f(x) = x^2 + 8x
To complete the square, we need to add and subtract (8/2)^2 = 16 to the expression:
f(x) = x^2 + 8x + 16 - 16
f(x) = (x + 4)^2 - 16
Now we have the function in vertex form:
f(x) = (x + 4)^2 - 16
The axis of symmetry for a quadratic function in vertex form y = a(x-h)^2 + k is x = h. Therefore, the axis of symmetry for the function f(x) = (x + 4)^2 - 16 is x = -4.