I am on a planet whose acceleration due to gravity is g= 6 ft/s?. I'm standing on a cliff edge with altitude of a = = 80 ft above the ground and I throw an object straight up at a velocity of v = 20 ft/s. The equation y = -; 1. 5gt2 + vt +a gives the height y of the object t seconds after I throw it. The graph of height versus time will be a parabola. -Find the exact vertex of the parabola. (Give both coordinates as rational numbers.) What does the vertex repre- sent in the context of this problem? -Find the exact time in seconds when the object will land on the ground, then approximate it to four decimal places.

Q: Find the equation of the parabola and put it in the form f(x)= ax^2 +bx+c  Given:  Vertex: (2/3 ,…

A:

Q: Find the parabola with equation y=x^2+bx+c that has slope of 8 when x=9 and passes through the…

A:

Q: Find the coordinates of the vertex of the parabola y = x^2 - 4x + 1 using derivatives O (2, -3) O…

A: To find the vertex of the parabola by using derivatives

Q: Find a parabola with equation y = ax2 + bx + c that has slope 8 at x = 1, slope −12 at x = −1, and…

A:

Q: At what point does the line normal to the graph of y=5−4x+4x2 at (1,5) intersect the parabola a…

A: The given function is- y=5-4x+4x2.................1 Differentiating the above expression w.r.t. x-…

Q: Find a parabola with equation y = ax2 + bx + c that has slope 11 at x = 1, slope -25 at x = -1, and…

A:

Q: Find the standard equation of the parabola with x intercepts at x = 2 and x -3, and a y-intercept at…

A: Solution is given below

Q: Find a parabola with equation  y = ax2 + bx + c  that has slope  13  at x = 1, slope  −19  at x =…

A:

Q: The vertex of a parabola is located at (−5, 6). If the parabola has a y-intercept of (0, 231), which…

A:

Q: What is the general equation of a parabola that opens upward with V(-1,2)?

A: The general equation of the parabola opening upwards is x-h2=4py-k where (h,k) is vertex. here…

Q: In the xy-plane, a line that has the equation y = c for some constant c intersects a parabola at…

A: in the xy-plane a line that has the equation y=c for some constant c intersects a parabola at…

Q: If a person shoots a basketball overhand from a position 8 feet above the​ floor, then the path of…

A: The path of the basketball through the hoop is modeled by the parabola,

Q: How many common points does the parabola y=x2-2x-2 have with the straight line a) y=2x-6; b) x-…

A: Solving two equations

Q: Find the point on the parabola y* = 2x that is nearest the point (1, 4).

A:

Q: Suppose you are given the x-coordinate of a point on a parabola. How can you find the matching…

A: According to Bartleby guidelines, only one question can be solved at a time. Kindly post other…

Q: -16х2 %3D 0.117 р2 y +2.75х + 3

A: Given, v =  29.97285 y = -16x20.117v2 + 2.75x +3 y at  v =  29.97285 y = -16x20.117(29.97285)2 +…

Q: Find the equation of the parabola with directrix x + 1 = 0, axis y = 2, and latus rectum 3.

A: Given :          The equation of directrix of the parabola is x + 1 = 0          The length of the…

Q: A parabolic arch has an equation of 3x 2 + y – 300 = 0. a) What is the maximum height of the arch?…

A:

Q: A hawk flying at 15 m / s at an altitude of 180 m accidentallydrops its prey. The parabolic…

A:

Q: The loft in Casa Batlló in Barcelona, contains a series of sixty catenary arches which closely…

A: To find width and tallness of the arch in parabolic shape

Q: Find the equation for the parabola that has its vertex at the 1 origin and has directrix at y 41…

A:

Q: Which is the equation of a parabola that has x-intercepts at (2,0) and (-6, 0)?

A:

Q: Find the equation of the parabola with directrix y = 3, axis x = 0, and latus rectum 4. (two answers…

A: The standard equation of the parabola is (y-k)=4a(x-h)2, where h and k are the coordinates of the…

Q: A hawk flying at 18 m/s at an altitude of 190 m accidentally drops its prey. The parabolic…

A: Given that: y=190-x254 Let,  y=0190-x254=0190=x254x=101.29So  the  distance  travelled  is  the  one…

Q: Find a parabola with equation y= ax2 + bx +c that hasslope 4 at x=1  , slope -8 at x= -1 , and…

A: The parabola is y=ax2+bx+c. It has a slope of 4 at x=1 and slope of -8 at x=-1 and passes through…

Q: Find the point on the parabola y = (x – 3)² – 5 that is closest to the point (0,0). |

A:

Q: A cannonball fired out to sea from a shore battery follows a parabolic trajectory given by the graph…

A:

Q: Find the point on the parabola y = x³ that is closest to the point (1, 2) with two digits accuracy…

A:

Q: 1. For the parabola equation: (y-2) = -3(x+4)^2 + 7, in which direction does the parabola open? *

A: We have to find the direction in which the given parabola opens.

Q: Find the point(s) of intersection of the parabola with equation y = x2 - 5x + 4 and the line with…

A: Given equations are,

Q: find the general equation of the parabola with horizontal axis which crosses the x-axis at x=2 and…

A:

Q: FInd the equations of the tangents with slope m=-2/9 to the ellipse 4x^2+9y^2=40

A:

Q: Use a graphing device to approximate to two decimal places, the value of x where the graphs of the…

A:

Q: Find the standard equation of a parabola if its latus rectum measures 9 units, axis at y = 3, p is…

A: Let's find standard equation of a parabola.

Q: Find the equation of the parabola with directrix x + 1 = 0, axis y = 2, and latus rectum 2.

A:

Q: Find the point on the parabola y 2 =2x that is closest to the  point ( 1, 4)

A: Given: y2=2x let's point on parabola is t22,t now, if point1,4 is closest to t22,t2 then product of…

Q: A hawk flying at 16 m/s at an altitude of 170 m accidentally drops its prey. The parabolic…

A:

Q: Find equations for two lines through the origin that are tangent to the ellipse x - 8x + y² + 5 = 0.

A:

Q: Find the points of intersection of the parabola with equation 2x + y² + 4y – 2 = 0 and the line…

A: Here we find the intersecting point of parabola and the line.

Q: Q3// Does the parabola y = 2x2 13x + 5 have a tangent whose slope is (-1)? %3D If so, find tangent…

A:

Q: Find the equation of the parabola with directrix y = 3, axis x = 0, and latus rectum 4

A: Given: Equation of directrix:y=3……1Equation of axis:x=0……2Length of latus rectum:4……3

Q: Find the equation of the parabola with directrix x + 2 = 0, axis y = 4, and latus rectum 4.

A:

Q: How many common points does the parabola y=x2-2x-2 have with the straight line a) y=2x-6; b) x-2y=4?

A:

Q: Describe how the parabolas y = x2 + bx change as b changes from -oo to oo.

A:

Q: Find the equation for the parabola that has its focus at (-53/4, -7) and has directrix x = 5/4.

A:

Q: Find the equation of the parabola whose vertex lies at (0,-2) and directrix at x=2

A:

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.