The question isn't for sure written, yet in keeping with what i think of this is meant to be: you have y = 20t - 16t^2, and y = 5. subsequently, 20t - 16t^2 = 5, which could be converted to: 16t^2 - 20t + 5 = 0 you may remedy this via in basic terms employing the quadratic formula: t = [20 +/- sqrt (20^2 - 4 (sixteen) (5))] / (2 (20)) do in basic terms the arithmetic, and you have got the respond.
Comments
you need to complete the squares:
2x^2- 16x -12y +20 = 0
*divide by 2*
x^2 - 8x -6y +10 = 0
*complete the square for "x"*
x^2 -8x + 16 - 16y + 10 -16 = 0
(x-4)^2 -16y -6 = 0
(x-4)^2 = 16y+6
(x-4)^2 = 4*4y + 2*3 = 4*4(y- (6/16)) = 4*4 ( y - (3/8))
so your h is 4, p is 4, k is (3/8)
good luck
First gather all x's to one side of equation, and the rest on the other side:
2x² - 12y - 16x + 20 = 0
2x² - 16x = 12y - 20
Factor out coefficient of x (on both sides), then simplify
2 (x² - 8x) = 2 (6y - 10)
x² - 8x = 6y - 10
Complete the square
x² - 8x + 16 = 6y - 10 + 16
(x - 4)² = 6y + 6
Factor out coefficient of y
(x - 4)² = 6(y + 1)
So we have h = 4, k = -1 and 4p = 6, p = 3/2
Vertex: (h,k) = (4,-1)
Focus: (h, k+p) = (4, 1/2)
Directrix: y = k-p → y = -5/2
The question isn't for sure written, yet in keeping with what i think of this is meant to be: you have y = 20t - 16t^2, and y = 5. subsequently, 20t - 16t^2 = 5, which could be converted to: 16t^2 - 20t + 5 = 0 you may remedy this via in basic terms employing the quadratic formula: t = [20 +/- sqrt (20^2 - 4 (sixteen) (5))] / (2 (20)) do in basic terms the arithmetic, and you have got the respond.
All such problems use "completing the square" and there is no "if possible" involved to determine the rest.
x=y