ch 4 review

Front

What is a solution to the system of inequalities: y < -1/2x + 3 and y < (x+1)^2?

Back

(2, 1)

Front

Identify the exception among the solutions to the inequalities: y < -1/2(x-1)^2 + 5 and -5 < y - x.

Back

(10, 1)

Front

Solve the system of equations: 6x^2 + 5y^2 = 38 and 7x^2 - 3y^2 = 9.

Back

(\sqrt{3}, 2), (\sqrt{3}, -2), (-\sqrt{3}, 2), (-\sqrt{3}, -2)

Front

Solve the inequality: x^2 - 3x > 2x.

Back

(-∞, 0) U (5, ∞)

Front

What is an extraneous solution in the context of equations?

Back

An extraneous solution is a solution that emerges from the process of solving an equation but does not satisfy the original equation.

Front

What does it mean for a system of equations to be inconsistent?

Back

A system of equations is inconsistent if there are no solutions that satisfy all equations simultaneously.

Front

How do you graph a system of inequalities?

Back

Graph each inequality on the same coordinate plane, shading the region that satisfies each inequality.

Front

What is the significance of the vertex in a quadratic inequality?

Back

The vertex represents the maximum or minimum point of the parabola, which helps determine the solution set for the inequality.

Front

Define a quadratic function.

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c.

Front

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

Back

The discriminant is given by b^2 - 4ac; it indicates the nature of the roots: positive (two real roots), zero (one real root), or negative (no real roots).