Mathematics, 15.07.2019 18:30, payshencec21

Complete the square in the quadratic function f given by f(x) = 2x2 - 6x + 4

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Completing the square is a way of factoring, and it is also a way to put a quadratic into vertex form to determine the vertex of the parabola. To begin completing the square, set the equation equal to 0 and then move the constant over by subtraction to get 2x^2-6x=-4 . The rule for completing the square is that the leading coefficient has to be a 1. Ours is a 2. So we have to factor it out. 2(x^2-3x)=-4 . We will take half the linear term, square it, and add it to both sides. Our linear term is 3. Half of 3 is 3/2 and 3/2 squared is 9/4. We add 9/4 inside the parenthesis. But outside is the 2 we factored out, hanging out front there, refusing to be ignored. It is a multiplier. That means what we have actually added in is 2*9/4 which is 18/4. That looks like this: $2(x^2-3x+\frac{9}{4})=-4+\frac{18}{4}$ . On the right we will do the addition there by finding a common denominator, but on the left we have, in this process, created a perfect square binomial, the whole point of this nightmare. That looks like this: $2(x-\frac{3}{2})^2=\frac{1}{2}$ . The only left to do, if you need to, is move the 1/2 back over to the other side of the equals sign and set the quadratic back equal to y. $2(x-\frac{3}{2})^2-\frac{1}{2}=y$ . The vertex of our parabola is (3/2, -1/2).

answered: Guest

1/3 + 1/3 ≠ 2/6 because 1/3 alone = 2/6

step by step explanation:

1/3 + 1/3 = 2/3 2/3=4/6

answered: Guest

First, think of what you know. you know that the number t the end of the equation will need to be subtracted because it is the money he lost from buying the lawn mower. and your first two weeks have negative profit, so that tells you that c and d are wrong. now you can plug any of the weeks into a and b to see which one works. i'll start with plugging week 1 into a. $y = 60(1) - 90 \\ y = 60 - 90 \\ y = - 30$ this isn't right because it says your answer for week one should be -90.so now we need to try the same thing with b. $y = 60(1) - 150 \\ y = 60 - 150 \\ y = - 90$ this one got you the right answer, (sometimes if you only check with one of the weeks multiple will work so you need to check with more of the weeks, but it worked out fine here)this means that b is the correct answer.let me know if you need more clarification. i hope this : )

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Complete the square in the quadratic function f given by f(x) = 2x2 - 6x + 4...