History[ edit ] Lodovico Ferrari is credited with the discovery of the solution to the quartic inbut since this solution, like all algebraic solutions of the quartic, requires the solution of a cubic to be found, it could not be published immediately. Depman claimed that even earlier, inSpanish mathematician Valmes was burned at the stake for claiming to have solved the quartic equation. Several attempts to find corroborating evidence for this story, or even for the existence of Valmes, have failed. The same is true for the intersection of a line and a torus.

Finding Quadratic Equation from Points or a Graph Quadratic applications are very helpful in solving several types of word problems other than the bouquet throwing problemespecially where optimization is involved. Again, we can use the vertex to find the maximum or the minimum values, and roots to find solutions to quadratics.

Note also that we will discuss Optimization Problems using Calculus in the Optimization section here. Find the highest point that her golf ball reached and also when it hits the ground again.

Find a reasonable domain and range for this situation. If units are in meters, the gravity is —4. Since we need to find the highest point of the ball, we need to get the vertex of the parabola.

Then we can use these two values to find a reasonable domain and range: This is the second root. We want the zero that is positive. We will discuss projectile motion using parametric equations here in the Parametric Equations section.

Quadratics Trajectory Path Problem: What is the maximum height the ball reaches, and how far horizontally from Audrey does is the ball at its maximum height?

How far does the ball travel before it hits the ground? To solve this, we should not expand the square out, but solve using the square root method; this Is much easier. Quadratic Application Problem A ball is thrown in the path, measured in feet: This means that the maximum height since the parabola opens downward is 8 feet and it happens 20 feet away from Audrey.

The ball will hit the ground We could have also used a graphing calculator to solve this problem. Optimization of Area Problem: What would be the dimensions length and width of the garden with one side attached to the house to make the area of the garden as large as possible?

What is this maximum area?

Also, what is a reasonable domain for the width of the garden? Area depends on length and width — which makes sense. We know the width has to be positive, which means it has to be greater than zero. The profit from selling local ballet tickets depends on the ticket price.

This problem is actually much easier since we are given the formula for the profit, given the price of each ticket. How much should the company charge for the purse so they can maximize monthly revenues?

Then we can find the maximum of our quadratic to get our answers. Here is our equation: Bunny Rabbit Population Problem: This answers a and b above.

For cwe need to see when the graph goes back down to 0; this is when there are no rabbits left on the island. To answer c above, the rabbit population will disappear from the island at around months from when the observations started.

OK, use your imaginations on this one sorry! Taylor and Miranda are performing on a magic dimension-changing stage that is 20 yards long by 15 yards wide.Write a quadratic equation with the given roots. Write the equation in the form ax^2+bx+c=0 where a, b, and c are integers.

- How to Write a Rebuttal for Teachers by stylecampaign. views. P 16 01 Writing a quadratic equation given the roots and the leading coefficient, Finding a Quadratic Equation Given the Roots a, Aleks - Finding the roots of a quadratic with leading coefficient greater than 1, How-To Find A Quadratic Equation Given The Roots .

Just as a quadratic equation can map a parabola, the parabola's points can help write a corresponding quadratic equation.

With just two of the parabola's points, its vertex and one other, you can find a parabolic equation's vertex and standard forms and write the parabola algebraically. How to Write Quadratic Equations Given a Vertex.

The roots or solutions of a quadratic equation are its factors set equal to zero and then solved for x. When roots are given and the quadratic equation is sought, write the roots with the correct sign to give you that root when it is set equal to zero and solved.

For example, a quadratic equation has a root of -5 and +3. Home; Calculators; Algebra I Calculators; Math Problem Solver (all calculators) Slope Intercept Form Calculator with Two Points.

The slope intercept form calculator will find the slope of the line passing through the two given points, its y-intercept and slope-intercept form of the line, with steps shown. Write the quadratic equation whose roots are and -8 with a vertex of (-9, -1).

Quadratic equations are in the form `ax^2 +bx+c=0` where a,b, and c are real numbers and a is not equal to 0.

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Finding a Quadratic Equation given the roots