What properties makes the equation ture?
1 answer:
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Answer:
Step-by-step explanation:
Your final answer is the standard form of a parabola. Since your equation has an x-squared term in it and not a y-squared term, your form will be
To get it into this form we will solve the quadratic for y and then set it equal to 0 so we can complete the square on it. Solving for y then setting y equal to 0:
so
We only need to complete the square on the x-terms, so we will move the constant back over to the other side of the equals sign:
The rule for completing the square is that the leading coefficient HAS to be a 1. Ours is 1/8, so we have to factor it out. When we do that we are left with:
To complete the square on the left, we take half the linear term, square it, and add it onto both sides. Our linear term is 2 (the number stuck to the x-term). Half of 2 is 1, and 1 squared is 1. So we add it into the parenthesis on the left. BUT we cannot discount the 1/8 sitting out front there. It is a multiplier. So what we actually added on the left is 1/8(1). That looks like this:
Now we will write the left side into its perfect square binomial (which was the whole reason for doing this!) and simplify the right at the same time:
Now we will set the whole thing back to equal y:
That's one form. But you need it in vertex form, so we add 3 to both sides:
and then multiply both sides by 8:
If you need to break it down further to include what your p value is, then:
Either that one or the one right above it should work.