Algebra 2 Review

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on the direction it opens. It can be found using the formula (-b/2a, f(-b/2a)) for the quadratic function f(x) = ax² + bx + c.

Front

How do you find the x-intercepts of a quadratic function?

Back

To find the x-intercepts of a quadratic function, set f(x) = 0 and solve the equation ax² + bx + c = 0 using factoring, completing the square, or the quadratic formula x = (-b ± √(b² - 4ac)) / (2a).

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions (roots) of the quadratic equation ax² + bx + c = 0.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac. It determines the nature of the roots: if positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

What is a linear equation?

Back

A linear equation is an equation of the first degree, which means it can be written in the form ax + b = 0, where a and b are constants and a ≠ 0.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the slope of a line given two points?

Back

The slope (m) of a line given two points (x₁, y₁) and (x₂, y₂) is calculated using the formula m = (y₂ - y₁) / (x₂ - x₁).

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. Solutions to the system are the values that satisfy all equations simultaneously.

Front

What is the method of substitution in solving systems of equations?

Back

The method of substitution involves solving one equation for one variable and then substituting that expression into the other equation to find the values of the variables.