Complete the square to re-write the quadratic function in vertex form:
y=7x
2
−126x+566
To complete the square, we will need to focus on the quadratic term, which is -126x.
Step 1: Divide the coefficient of the linear term by 2, and then square it:
(-126 / 2)^2 = 63^2 = 3969
Step 2: Add the result from step 1 to both sides of the equation. This will ensure that the quadratic term becomes a perfect square trinomial.
y + 3969 = 7x^2 - 126x + 3969 + 566
Simplifying the right side:
y + 3969 = 7x^2 - 126x + 4535
Step 3: Rewrite the right side of the equation as a perfect square trinomial by factoring:
y + 3969 = 7(x^2 - 18x + 648)
Step 4: Continue simplifying the right side:
y + 3969 = 7(x - 12)^2
Step 5: Subtract 3969 from both sides of the equation to isolate y:
y = 7(x - 12)^2 - 3969
Therefore, the quadratic function in vertex form is:
y = 7(x - 12)^2 - 3969