quadratic and liner equations

Question 1

What is the general form of a quadratic equation?

Answer 1

The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Question 2

True or False: A linear equation can be represented in the form y = mx + b.

Answer 2

True

Question 3

Fill in the blank: The solution to a system of linear equations is called a _____.

Answer 3

solution set

Question 4

What method can be used to solve simultaneous linear and quadratic equations?

Answer 4

Substitution or elimination method.

Question 5

If a quadratic equation intersects a linear equation at two points, how many solutions does the system have?

Answer 5

Two solutions.

Question 6

Multiple choice: What is the maximum degree of a polynomial in a quadratic equation? (A) 1 (B) 2 (C) 3

Answer 6

B

Question 7

What is the discriminant in a quadratic equation and what does it indicate?

Answer 7

The discriminant is b^2 - 4ac; it indicates the nature of the roots: if positive, two distinct real roots; if zero, one real root; if negative, two complex roots.

Question 8

True or False: The graph of a linear equation is always a straight line.

Answer 8

True

Question 9

What is the vertex of a parabola represented by a quadratic equation?

Answer 9

The vertex is the point (h, k) where the parabola changes direction, given by the formula h = -b/(2a) and k = f(h).

Question 10

Fill in the blank: The intersection points of a quadratic and a linear equation can be found by _____.

Answer 10

solving the equations simultaneously