The altitude of a kicked football can be described with the function h(?) = −0.01x^2 + 1.18x^2 + 2, where x, in feet, is the horizontal distance from the point of impact with the punter’s foot. a. Find the vertex of the parabola. b. If the opposite team does not catch the ball, how far away from the kicker does the ball hit the ground? c. What is the maximum height of the ball?

Q: What is the maximum point on the curve = 2 + 12? − x3

A: Maxima minima problem

Q: Write an equation of the parabola that has the same shape as the graph of f(X)=3^2, but with a (7,6)…

A: The general equation of a parabola in vertex form is y=ax-h2+k. It is given that the required…

Q: Suppose the x-intercepts of a parabola are -1 and 5. Q) write a quadratic function with these…

A: Given query is to find the quadratic equation of with x intercepts.

Q: Determine the axis of symmetry of the graph of the following parabola. f(x)=5^x2+190x+19

A: To determine the axis of symmetry of the graph of the following parabola.

Q: Find the area of the largest rectangle with one corner at the origin, the opposite corner in the…

A:

Q: Which point is the vertex of the parabola y = 6(x+3)^2 - 5?

A:

Q: How do you find the vertical stretch or shrink of a square root equation on a graph

A: Explained below

Q: Does the values of y have to be the same in axis of symmetry and vertex in functions when they are…

A:

Q: A parabola has a vertex at (4,-11) and runs through the point (8,-123). Determine the equation for…

A:

Q: raph the quadratic function given in standard form

A: given vertex given ( -2 , -1 )

Q: Graph the quadratic (parabola). Y=-x^2+x+6

A: We have to draw the graph

Q: A soccer ball is hit from the ground and lands 12 meters away from where it was hit. Further- more,…

A: Solve the given problem

Q: 4. A small company has determined that its profit ("P") depends on the money spent on publicity 8x…

A: The profit function is : The income function is :Where P represents profit and x represents the…

Q: Identify the vertex of the parabola F(x) = (x - 9)2 - 7

A:

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.