# Write a quadratic function in vertex form for the parabola

Features of quadratic functions Video transcript I have an equation right here. It's a second degree equation. Finding Quadratic Equations 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.

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?

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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?Lesson 6 Graphing Quadratic Functions.

## Math Questions . . . Math Answers . . .

The term quadratic comes from the word quadrate meaning square or rectangular. Similarly, one of the definitions of the term quadratic is a square. In vertex form, a quadratic function is written as y = a(x-h) 2 + k See also Quadratic Explorer - standard form. In the applet below, move the sliders on the right to change the values of a, h and k and note the effects it has on the graph.

(We will discuss projectile motion using parametric equations here in the Parametric Equations section.). Note that the independent variable represents time, not distance; sometimes parabolas represent the distance on the \(x\)-axis and the height on the \(y\)-axis, and the shapes are leslutinsduphoenix.com versus distance would be the path or trajectory of the bouquet, as in the following problem.

Note that the denominator is then 2a instead of 2c. Some common examples of the quadratic function. Notice that the graph of the quadratic function is a parabola. The calculator works well, fast typing, and does what it supposed to do.

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Solving Quadratics by Factoring and Completing the Square – She Loves Math