To convert the quadratic function f(x) = x² – 8x + 3 into vertex form, we can use the method of completing the square.
1. Start with the function:
f(x) = x² – 8x + 3
2. Focus on the quadratic and linear terms, which are x² – 8x. To complete the square, we need to find a number that makes this a perfect square trinomial.
3. Take the coefficient of x (which is -8), divide it by 2, and then square it:
(-8 / 2)² = (-4)² = 16
4. Add and subtract this number (16) within the function:
f(x) = (x² – 8x + 16) – 16 + 3
5. Now, rewrite the expression:
f(x) = (x – 4)² – 13
Now we have the function in vertex form:
f(x) = (x – 4)² – 13
This shows that the vertex of the parabola represented by this function is at the point (4, -13).