Parabola Questions and Answers

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A parabola whose axis is parallel to the y-axis passes through the points (1,1), (2,2) and (-1,5). Find the equation of the parabola.

Convert from standard to vertex form: (x + 5)(x + 4)

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Find the x-and y-intercepts for the parabola -3x^2+6x+9=0

Find the values of x that are solutions to f(x)= 0. f(x)= -5x^2 + 7x + 2

Find the average height of the paraboloid z = 10 x^2 + 4 y^2 above the annular region 4 less than or equal to x^2 + y^2 in the xy-plane. (a) 596 / 3. (b) 595 / 2. (c) 510. (d) 765/2.

Let \vec{F}= -xy\vec{i} + y\vec{j} and C be the piecewise path as shown. The bottom curve is a parabola. Set up the iterated integral resulting from Green's Theorem.

The reflector of a searchlight is in the shape of a paraboloid of revolution. Its diameter is 12 inches and its depth is 9 inches. How far from the vertex should the light bulb be placed so that the r

How do you convert standard form to general form of a parabola?

For a parabola y = -(x - 1/2)^2 + 25/4, determine the following and sketch a rough graph. (i) Does it open up or down? (ii) y-intercept (iii) vertex (iv) axis of symmetry (v) domain and range (vi) ver

A car is traveling along a highway shaped like a parabola with its vertex at the origin. The car starts at 100 miles north and 100 miles west. There is a statue at 100 miles east and 50 miles north. A

Sketch the graph of y=x^2-10. Use the method of Lagrance multipliers to find the points on the curve that are closest to the origin. Don't round off your answer, it will involve square roots.

A point in the first quadrant lies on the parabola y = x . Express the coordinates of P as function of the angle of inclination of the line joining P to the origin.

Find an equation of the parabola y = ax^2 + bx + c that passes through (0, 4) and is tangent to the line y = 5x - 5 at

What is the graph of y = 3x^2?

How do I find the standard form for y= 2(x+2)^2 -5?

Given y=2x^{2}4x-1 Plot,find the vertex,focus and the equation of the directrix line.

Find an equation for the ellipse that shares a vertex and a focus with the parabola x^2 + y = 100 and that has its other focus at the origin.

Boat A leaves the dock at 12 pm heading due South at a constant speed of 20 km/h. Meanwhile, at 12 pm Boat B, a pirate ship, is 15 km due West of the dock where boat A started, and is sailing due East

A parabola, f, intersect the x-axis at A and B and the y-axis at C. The axis of symmetry of the parabola has the equation x=-3. The line through A and C has the equation g(x) = x+7. Determine the coo

Let m and b be nonzero real numbers. If the line y = mx+b intersects y^2 = 4px at only one point, show that p = mb.

A parabola ,f, intersect the x axis at A and B and the y axis at C. The axis of symmetry of the parabola has the equation x= -3.The line through A and C has the equation g(x)=x+7. Determine the coordi

If the line y = mx - 5 does not meet the curve y = 3x^2 - 6x + 7 then value of m is in the open interval (a,b). Find the exact value of b.

Show that the parabolas r = c / (1 + cos theta) and r = c / (1 - cos theta) intersect at right angles.

A parabola is the collection of points (x, y) whose distance from (3, 4) is the same as the distance from the line y = 2. Which form does the equation of the given parabola fit? A. (x - h)^2 = 4c(y

What is the axis of symmetry for a parabola, expressed by the quadratic equation, 2x^2-8x+11?

A window is designed to be the area between a parabolic section and a straight base. The height is 0.640 m and the base is 1.60 m. What is the area of the window?

Two lines through the point (1, -3) are tangent to the curve y = x^2. Find the equations of these two lines and make a sketch to verify your results.

Identify the type of curve and sketch the graph of y^2 - 2x + 6y + 5 = 0.

y = x^2 - 11x + 30 For what values of x is y \geq 0?

Determine the open intervals on which the graph of f(x) = -7x^2 + 8x + 1 is concave downward or concave upward.

A parabolic arch bridge has a 60 ft base and a height of 24 ft. Find the height of the arch at a distance of 5, 10, and 20 ft from the center.

The subtangent, ordinate and subnormal to the parabola y^2 = 4 - x at a point (different from the origin) are in: (a) A.P. (b) G.P. (c) H.P. (d) None of these

What is the shape of a quadratic equation called?

What does the graph of a quadratic equation look like?

Who invented standard form in math?

Find the parabola whose minimum is at (7,6). The parabola's equation is y = x2 + ax + b, where a = and b =

Explain how to find a vertical stretch when given 2 coordinate points, one is the vertex and the other is a point that the parabola passes through.

Sketch the surface: y=x^2-z^2

Find the least squares solution for the following problem: A parabola y = ax^2 +bx +c is to pass through the points (1, 2), (-1,3), (0,4),(2,-1).

What does a represent in a quadratic equation?

A wave entering parallel to the axis of a radio wave antenna with a parabolic cross section is reflected through the focus. The vertex of the parabola is at the origin, and the directrix is a vertical

Find a fully simplified equation for the set of all points P=(x,y) equidistant from the x-axis and the point (0,-4). Plot a graph of this set of points and describe this set geometrically.

Draw part of the surface represented by z = y^2 in 3-dimensional space.

Sketch and shade the region bounded by the graphs of the functions. y=10-x^2, y=x^2

Find the eccentricity and classify the conic. Sketch the graph and label the vertices. r=\frac{6}{2+2\cos \theta}

How do you find the focus of a parabola in vertex form?

For the quadric surface given by 4x^2 - 4y^2 - 8y = z, sketch the level curves for x = 0, x = plus or minus 1, x = plus or minus 2. then Identify the shape.

Find the center, foci, vertices, asymptotes, and radius, as appropriate of the conic sections. Then, sketch the graph. x^2 + 2x + 4y - 3 = 0

Draw a diagram to show that there are two tangent lines to the parabola y = x^2 that passes through the point (0, -9). Find the coordinates of the points where these tangent lines intersect the para

How do you move a parabola horizontally in standard form?

Determine the position of the vertex, the opening and the equation of the axis of symmetry for the graph of the quadratic equation f(x) =3(x-1)^2 - 5

The line y = x + 6 intersects the parabola y = x^2 at two points A and B. Find the point C on the parabola between A and B such that the triangle ABC has maximum area.

A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating the curve y = ax^2 about the y-axis. If the dish is to have a 6 ft diameter and a maximum depth of 2

Find an equation for theparabola that has its vertex at the origin and satisfies the given conditions Focus at the positive x-axis and away from the directrix

Determine the symmetry, if any, of the following: (a) f(x) = .75x^2 + |x| + 1 \\ (b) f(x) = x^4 - 5x + 2

Find the parabola with equation y = ax^2 + bx whose tangent line at (1, 0) has equation y = 5x - 5.

Find the vertex, foucs, and the directrix of the parabola, give a sketch of graph. y^{2}+4y+8x=12=0 Please show steps to answer: Vertex (2,-2), foucs (0, -\frac{1}{2}), directrix x=\frac{1}{2} Thanks

Show that any two tangent lines to the parabola y = ax^2 intersect at a point that lies on the vertical line halfway between the point of tangency.

An arrow is shot straight upward from the ground - the height at time t is given by 16t^{2}+80t (a) Find the velocity when t = 1 (b) How high does the arrow go?

Determine the equation of the parabola, whose axis of symmetry is the x-axis, passing through (-2, 4) vertex is the origin. Find the focus and directrix.

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