8.1k views
5 votes
Which of the following equations are quadratic equations? Explain how you know

y = -2(x - 3)2 – 5,
f(3) = V2+4 - 4,
7x2 + 3y = 12
202 + 3y2 = 12

1 Answer

4 votes

Final answer:

The equation y = -2(x - 3)^2 – 5 is a quadratic equation because it has a squared term. The equation 7x^2 + 3y = 12 is quadratic in x due to the x^2 term. The equation 20x^2 + 3y^2 = 12, while not a standard one-variable quadratic equation, also falls under the family of quadratics since both x and y are squared.

Step-by-step explanation:

The equations to be analyzed for their quadratic nature are y = -2(x - 3)^2 – 5, 7x^2 + 3y = 12, and 20x^2 + 3y^2 = 12. A quadratic equation is an equation of the second degree, which means it includes at least one term that is squared. The standard form of a quadratic equation in one variable is ax^2 + bx + c = 0, where a, b, and c are constants, and a is not equal to 0.

The first equation, y = -2(x - 3)^2 – 5, is a quadratic equation because it has the term (x - 3)^2, which is the square of a binomial, indicating that x is raised to the second power.

The second equation, 7x^2 + 3y = 12, is a quadratic equation in x because it includes the x^2 term.

The third equation, 20x^2 + 3y^2 = 12, is not a standard quadratic equation in one variable, but it is a quadratic in two variables because both x and y are squared. It is therefore part of the family of quadratic equations, but not a pure quadratic equation in the sense of having a single variable squared.

User Paras Joshi
by
8.3k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories