Parabola Questions and Answers

Consider the parabola given by the equation: f(x) = 4x² – 10x-4 Find the following for this parabola: A) The vertex: B) The vertical intercept is the point C) Find the coordinates of the two x intercepts of the parabola and write them as a list, separated by commas:

NASA launches a rocket at t = 0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t) = − 4.9t² + 103t + 192. Assuming that the rocket will splash down into the ocean, at what time does splashdown occur? The rocket splashes down after seconds. How high above sea-level does the rocket get at its peak? The rocket peaks at meters above sea-level.

The height y (in feet) of a ball thrown by a child is y=-1/14 x² + 2x + 3 where is the horizontal distance in feet from the point at which the ball is thrown. (a) How high is the ball when it leaves the child's hand? feet (b) What is the maximum height of the ball? feet (c) How far from the child does the ball strike the ground? feet

Find the reflection of the function y = x² over y-axis. The reflection along the y-axis is (-x)². The reflection along the y-axis is x³. The reflection along the y-axis is -x².

Describe the transformations to the parent function. Check all boxes that apply. f(x)=1/3(x - 2)² Reflects across the x-axis (open down) Stretched by a factor of 3 (Narrower) Compressed by a factor of 3 (Wider) shifts right 2 shifts left 2 shifts up 2 shifts down 2

Find the x-intercept(s) and the coordinates of the vertex for the parabola y=x²-4x-5. If there is more than one x-intercept, separate them with commas.

Write the equation of a parabola whose directrix is a = (0.75, 4). 3.25 and has a focus at

Use the information provided to write the vertex form equation of each parabola. Vertex: (-7,-5), Focus: (-7,-41/8) y = (x +9) ² - 7 y = 2(x - 5)² +7 y- 1/2(x-5)²-7 y = -2(x+7)² - 5 y = 1/2( x − 4 )² + 6

Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep safe. Since Dr. Jones is a mathematician, she suggests building fences described by y = 112² and y = x² + 4. Farmer Jones thinks this would be much harder than just building an enclosure with straight sides, but he wants to please his wife. What is the area of the enclosed region?

Identify the surface defined by the following equation. 16z² + y² = 9 The surface defined by the equation is _____

Find the equation of the parabola described below. Find the two points that define the latus rectum, and graph the equation. Focus at (-3,6); directrix the line y = 4 The equation of the parabola in the standard form is (Type an equation.)

Given the function g(x) = -(x-3)² - 2. Determine if the function has a maximum or minimum and what are the coordinates of the vertex? a. (-3, -2) minimum b. (3,-2) maximum c. (-3, -2) minimum d. (3, 2) maximum

Find the y-intercept of the parabola. f(x) = -2x^2-12x-10

The mirror in an automobile headlight has a parabolic cross-section with the light bulb at the focus. On a schematic, the equation of the parabola is given as x^2= 4y. if we want to construct the mirror so that the focus is located at (0,1.25), what is the equation of the parabola?

Sketch the graph of the quadratic function and the axis of symmetry. State the vertex, and give the equation for the axis of symmetry. h(x) = (x + 3)^2 Use the graphing tool to graph the function as a solid curve and the axis of symmetry as a dashed line. Click to enlarge graph. The vertex is ____. (Type an ordered pair.) The axis of symmetry is _______. (Type an equation.)

An arch is in the shape of a parabola. It has a span of 800 feet and a maximum height of 40 feet. Find the equation of the parabola (assuming the origin is halfway between the arch's feet).Determine the height of the arch 143 feet from the center.