100 POINTS! I need a thorough word problem that includes a quadratic formula. PLEASE!!!! I will give brainliest if you provide a clear explanation, as well. I really appreciate it :))

Quadratic equations are actually used in everyday life, as when calculating areas, determining a product's profit or formulating the speed of an object. Quadratic equations refer to equations with at least one squared variable, with the most standard form being ax² + bx + c = 0.

Here is an example:

Antoine stands on a balcony and throws a ball to his dog, who is at ground level.

The ball's height (in meters above the ground), xxx seconds after Antoine threw it, is modeled by:

h(x)=-2x^2+4x+16h(x)=−2x

2

+4x+16h, left parenthesis, x, right parenthesis, equals, minus, 2, x, squared, plus, 4, x, plus, 16

What is the height of the ball at the time it is thrown?

____meters

here is another example:

2x2 + 5x + 3 = 0 = In this one a=2, b=5 and c=3

Hope that was helpful.Thank you!!!

ricchad ricchad · Answer 2 · 2020-09-09T21:33:12+02:00

Answer:

see below

Step-by-step explanation:

Often, the simplest way to solve "ax2 + bx + c = 0" for the value of x is to factor the quadratic, set each factor equal to zero, and then solve each factor. But sometimes the quadratic is too messy, or it doesn't factor at all, or you just don't feel like factoring. While factoring may not always be successful, the Quadratic Formula can always find the solution.

The Quadratic Formula uses the "a", "b", and "c" from "ax2 + bx + c", where "a", "b", and "c" are just numbers; they are the "numerical coefficients" of the quadratic equation they've given you to solve.

The Quadratic Formula is derived from the process of completing the square, and is formally stated as:

The Quadratic Formula: For ax2 + bx + c = 0, the values of x which are the solutions of the equation are given by:

-b ± [tex]\sqrt{b^2 - 4ac}[/tex]

x = ----------------------------------

2a