How do you graph this?

Question

d=50+312t-16^2

Answer 1

put t on the horizontal (x) axis, d on the vertical (y) axis

It's a downward opening parabola

take the derivative and set = 0, solve for t to find the vertex or max point

32t=312

t = 312/32 = 9.75 t=9.75 is the line of symmetry

-16t^2 +312t + 50 =0

8t^2 - 156t - 25 = 0

t = 156/16 + or - (1/16) sqr(156^2 + 64(50))

t = about 20.12 or -0.2 = the t (or x) intercept, = the points (-0.62,0) and (20.1,0) the line of symmetry is a vertical line through their midpoint or x = (19.7--1.5)/2 = . x=9.75 is the line of symmetry and 9.75 is the x coordinate of the vertex and of the maximum point of the parabola. y intercept = (0,50)

plug x=9,75 into the original equation to find the d or y coordinate of the vertex

-16(9.75)^2 + 312(9.75) + 50 = 0

d = 1571

vertex or max point is (9.75,1571)

plot the vertex, and 3 intercepts and draw a smooth curve through them, with the side to the right of the line of symmetry the mirror image of the left side

Answer 2

the following assumes you meant to write -16t^2, not -16^2. the -16 suggests gravity deceleration in feet per second per second. then the coefficient of the t term is initial velocity and the constant term, 50, is initial distance.

put t on the horizontal (x) axis, d on the vertical (y) axis

It's a downward opening parabola

take the derivative and set = 0, solve for t to find the vertex or max point

32t=312

t = 312/32 = 9.75 t=9.75 is the line of symmetry

-16t^2 +312t + 50 =0

8t^2 - 156t - 25 = 0

t = 156/16 + or - (1/16) sqr(156^2 + 64(50))

t = about 20.12 or -0.2 = the t (or x) intercept, = the points (-0.62,0) and (20.1,0) the line of symmetry is a vertical line through their midpoint or x = (19.7--1.5)/2 = . x=9.75 is the line of symmetry and 9.75 is the x coordinate of the vertex and of the maximum point of the parabola. y intercept = (0,50)

plug x=9,75 into the original equation to find the d or y coordinate of the vertex

-16(9.75)^2 + 312(9.75) + 50 = 0

d = 1571

vertex or max point is (9.75,1571)

plot the vertex, and 3 intercepts and draw a smooth curve through them, with the side to the right of the line of symmetry the mirror image of the left side

Answer 3

Vertex form has irrational numbers.

The alternative is to substitute several ordered pairs and sketch the graph.

Answer 4

I would first simplify the equation d=50+312t-16^2, which simplifies to d=312t-206. Then we have equation in slope-intercept form (y=mx+b). To make it easier to see will let d=y and t=x. Then we have y=312x-206. Our next step is to plot 2 points on the line. We know the y-intercept is at (0,-206) and we can put in a second value for x and solve the equation to find the y-value for our second point on the line. We then draw a straight line extending between the two points.

Answer 5

d=50+312t-16^2

d t

0 -146

1 166

2 478...............