Mathematics, 17.07.2019 20:00, tynitenaire

What are the coordinates of the focus of the parabola? y=−1/16x^2 − x + 2 (−8, 2) (8, 2) (8, 10) (−8, 10)

Answers: 1

Show answers

Answers

This is a tough one. the general form of a parabola is $(x-h) ^{2} =4p(y-k)$ , where h and k are the coordinates of the vertex and p is the distance from the vertex to the focus. In order to get our parabola into this form and solve for p (which will give us our focal point), we have to complete the square. Set the parabola equal to 0, then move over the constant to get this equation: $- \frac{1}{16} x^{2} -x=-2$ . In order to complete the square, the leading coefficient on the squared term has to be a +1. Ours is a $- \frac{1}{16}$ , so we have to factor that out of the x terms. When you do that you end up with $- \frac{1}{16} ( x^{2} +16x)=-2$ . Now we can complete the square by taking half the linear term, squaring it, and adding it to both sides. Our linear term is 16, so half of 16 is 8 annd 8 squared is 64. HOWEVER, on the left side, that $- \frac{1}{16}$ is still hanging out in front, which means that when we add in 64, we are actually adding in $- \frac{1}{16} *64$ which is -4. Now here's what we have: $- \frac{1}{16} ( x^{2} +16x+64)=-2-4$ which simplifies to $- \frac{1}{16}( x^{2} +16x+64)=-6$ . Creating the perfect square binomial on the left was the point of this (to give us our vertex), so when we do that we have $- \frac{1}{16} (x+8) ^{2} =-6$ . Now just for simplicity, we will take baby steps. Move the -6 back over by addition and set it back equal to y: $- \frac{1}{16}(x+8) ^{2}+6=y$ . Now we will work on getting into standard form. Move the 6 back over by the y (baby steps, remember) to get $- \frac{1}{16} (x+8) ^{2} =y-6$ . Multiply both sides by -16 to get our "p" on the right: $(x+8) ^{2} =-16(y-6)$ . We need to use our "4p" part of the standard form to find the p, which is the distance from the vertex to the focus. 4p=-16, and p = -4. That means that the focus is 4 units below the vertex. Let's figure out what the vertex is. From our equation, the vertex is ( -8, 6), and since this is an upside-down opening parabola, the focus will be aligned with the x-coordinate of the vertex. So our focus lies 4 units below 6 (6 is the y coordinate of the vertex which indicates up and down movement), so our focus has coordinates of (-8, 2), the first choice above. Told you it was a tough one! These conics are quite challenging!

answered: Guest

The answer is 1 because you have to flip the sign when dividing by negative number and 3

answered: Guest

translate k to n and reflect across the line containing jk.

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 19:40, josecano2

Which of the following could be the ratio of the length of the longer leg 30-60-90 triangle to the length of its hypotenuse? check all that apply. a. 313 6 b. 3: 215 c. 18: 13 d. 1: 13 e. 13: 2 of. 3: 15

Answers: 3

continue

Mathematics, 21.06.2019 21:30, mrlepreqon8897

Apool measures 100 meters by 100 meters a toddler inside the pool and trows a ball 60 centimeters from one edge of the pool. how far is the ball from the opposite edge of the pool

Answers: 1

continue

Mathematics, 21.06.2019 23:00, noahdwilke

36x2 + 49y2 = 1,764 the foci are located at: (-√13, 0) and (√13,0) (0, -√13) and (0,√13) (-1, 0) and (1, 0)edit: the answer is (- the square root of 13, 0) and (the square root of 13, 0)

Answers: 1

continue

Mathematics, 22.06.2019 00:00, mkay78

Apassenger train and a freight train leave san jose at 3pm, traveling in the same direction. the passenger train is going three times as fast as the freight train. at 6pm they are 240 miles apart. how fast is each travelling? explain your answer and show your

Answers: 1

continue

Do you know the correct answer?

What are the coordinates of the focus of the parabola? y=−1/16x^2 − x + 2 (−8, 2) (8, 2) (8, 10) (−...