Algebra 2 Semester 1 Final Review

Front

What is the process of completing the square in a quadratic equation?

Back

Completing the square involves rewriting a quadratic equation in the form of (x - p)^2 = q, where p and q are constants. This is done by adding and subtracting the square of half the coefficient of x.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is given by y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

Front

How do you find the vertex of a quadratic function given in standard form?

Back

For a quadratic function in standard form y = ax^2 + bx + c, the vertex can be found using the formula h = -b/(2a) and then substituting h back into the equation to find k.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation ax^2 + bx + c = 0 and is given by x = (-b ± √(b^2 - 4ac)) / (2a).

Front

What does the discriminant of a quadratic equation tell us?

Back

The discriminant, given by b^2 - 4ac, indicates the nature of the roots of the quadratic equation: if it's positive, there are two distinct real roots; if zero, there is one real root; if negative, there are two complex roots.

Front

How do you simplify the expression (3x)(3x^2 + 24x - 100)?

Back

Distributing gives 9x^3 + 72x^2 - 300x.

Front

What is the solution to the equation x^2 - 14x - 51 = 0?

Back

The solutions are x = 17 and x = -3.

Front

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

Back

The vertex represents the maximum or minimum point of the parabola, depending on the direction it opens.

Front

How do you solve a quadratic equation using the quadratic formula?

Back

Identify a, b, and c from the equation, substitute them into the formula x = (-b ± √(b^2 - 4ac)) / (2a), and simplify to find the roots.

Front

What is the standard form of a quadratic equation?

Back

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