4. Quarterback Cody can throw a football in a perfect parabolic arc to a receiver 40 yards downfield. Assume that Cody lets go of the ball 6 feet above the ground and the receiver catches it 6 feet above the ground. The ball reaches a maximum height of 16 feet above the ground halfway to the receiver. What is the equation of the path of the football? Show all your work and explain your reasoning.

Q: Find the standard equation of the parabola with directrix x + 1 = 0, axis y = 1 and the length of…

A: If the axis of parabola is y = 1, then the parabola is horizontal. As we know that the standard…

Q: What is the (unsigned) distance between the vertex and the focus of the parabola given by (x + 4)² =…

A: Given parabola equation,x + 42 = 19y + 5

Q: The parabola y = x² – 1 is constructed, but the axes are gone, somehow! With the help of ruler and…

A: Let us consider the function y=f(x) The transformation will shift the graph as  If y=f(x)+c and…

Q: Sasha plots the first two vertices of a right triangle in the coordinate plane. Where could she plot…

A: Given: Sasha plots the first two vertices of a right triangle in the coordinate plane To Find:…

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

A:

Q: A soccer ball is kicked from a point 23 m to the left of the half way line and lands at a point 17 m…

A: We use the equation in the form y=a(x-r)(x-s) Given Data: r=-23 and s=17

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: Show the complete solutions. Family of horizontal parabolas whose h to k ratio is 2.

A: Let's find differential equation.

Q: A suspension bridge with weight uniformly distributed along its length has twin towers that extend…

A: Here we have to calculate the height of cable

Q: A doomed ceiling is a parabolic surface. Ten meters down from the top of the dome, the ceiling is 15…

A: Given a doomed ceiling is a parabolic surface which is 10m down from top and 15m wide. A light is…

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: If the axis of symmetry of a parabola is given by x = 4, is it possible for the directrix to have…

A:

Q: 5. The equation of a family of parabolas with axis paralel to the y-axis is

A:

Q: What is the equation of the directrix of the parabola having a vertex at (6,0), passing through…

A: Given:- What is the equation of the directrix of the parabola having a vertex at (6,0), passing…

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

A:

Q: Exercise 2. Find a formula for the curve which is traced by the motion of a fixed point on a wheel…

A:

Q: What is the equation of parabola in standard form whose focus is at (-4,0) and the directrix is at…

A: Note that, the equation of the parabola with the directrix x+a=0 and the focus (a,0) is y2=4ax.

Q: A hamster wheel is in a cage on top of a table. If the high point of the wheel is 15 cm above the…

A: Using the given information draw a diagram and label it. From the figure, it is clear that the…

Q: 8. In general, if the line y = mx + b is rotated 90° about a point (x, mx + b), explain how you can…

A:

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

A: The equation of directrix of the parabola is x+1=0. The length of the latus rectum is 3. The…

Q: The parabola y = x² is shifted up by 7 units and to the left by 1 unit. What is the equation of the…

A: Equation of parabola is given as y=x2. If the parabola is shifted by a units and to the left by b…

Q: Graphically, parabolas can be viewed as the set of all points whose distance from _____ is equal to…

A: Graphically, parabolas can be viewed as the set of all points whose distance from _____ is equal to…

Q: Janiah can throw a softball in a perfect parabolic arc which is 70 feet, if Janiah does not feel…

A: Given that:-  Janiah can throw a soft ball in a    perfect parabolic arc             pitcher…

Q: 1. What is the equation of the line to the parabola y = x2 + 5x +1 through the 15 point at

A: Given, Parabola  y=x2+5x+1 Point 12, 154

Q: Define the term parabola?

A: Given: The term parabola.

Q: Find the point on the parabola y=x^2 that is closest to the point (6,3) what is the distance between…

A: Given: To find the point on the parabola y=x2 that is closest to the point (6,3) what is the…

Q: What are the coordinates of the end points of the latus rectum of the parabola with equation a - 2z…

A: What are the coordinates of the end points of the latus rectum of the parabola with equation…

Q: Determine the points of intersection of the parabola y=2x^2 +12x +10 and the line y=4x+2

A: I am attaching image so that you understand each and every step.

Q: Suppose a golf ball is driven so that it travels a distance of 200 feet as measured along the ground…

A: Given:A golf ball travels a distance of 200 feet as  measured along the ground and reaches an…

Q: In the context of hyperbolic geometry, show that the segment joining the midpoints of two sides of a…

A: Given below clear explanation

Q: I llustiate and Sketch the equation of parabola ?f vertex

A: General equation of parabola is of form y2=4ax or x2=4ay

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

A:

Q: The filament lightbulb is a thin wire that glows when electricity passes through it. The filament of…

A: Given: The given reflector is 7 inches wide and 2 inches deep i.e. (x,y)=(2,3.5)

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

A:

Q: Assume the equation of a parabola and a line are given by y = x +2 x and y =3 x +6, respectively.…

A:

Q: I really don't get this geometry

A: To find: The perimeter of the Quadrilateral CDEF. Concept used: The tangent drawn from the same…

Q: 4. In general, if the line y is rotated 90° about (0, 0), explain how you can find the equation of…

A:

Q: A tunnel through a mountain for a four lane highway is to have an elliptical opening. The total…

A: Given information: A tunnel through a mountain for a four lane highway is to have an elliptical…

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 from the hoop is modeled by the parabola,

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

A:

Q: The parabolic antenna has an equation of y^2 + 8x = 0. Determine the length of the latus rectum.

A: Here we use the standard form of parabola.

Q: Find the shortest distance of the point (10,4) to the parabola y=x2

A: Consider a  point on parabola  y=x2. Distance of this point with (10,4) s2=(x-10)2+(y-4)2…

Q: Plot both the following curves on the same set of axes. r = 5 − 4cos(θ), and the parabola y = x².

A: We have to Plot both curves on the same set of axes. r = 5 − 4cos(θ), and the parabola y = x².

Q: Suppose that two microphones 1500 m apart at points A and B detect the sound of a rifle shot. The…

A: Frist draw a diagram with given information as shown in below figure.

Q: Is this curve a twisted cubic, parabola, line, or helix?

A: The objective is to check whether the curve is a  twisted cubic, parabola, line, or helix.…

Q: What will be the equation of hyperbola that satisfies the given condition foci at (+ 24,0) and the…

A:

Q: An elliptical room is designed to function as a whispering gallery.  If the room is 30 feet long and…

A: We have to optimize the whispering effect of elliptical room, which is 30 feet long and 24 feet…

Q: Suppose a golf ball is driven so that it travels a distance of 200 feet as measured along the ground…

A:

Q: A parabolically shaped bookshelf has a width of 14 feet 8 inches at the top and height 8 ft. 4 in..…

A: Consider the given information as, width=14feet  8 inches and height =8ft 4 in

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.