Algebra 2 SOL Review #2

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation in the form ax² + bx + c = 0. It is given by: x = (-b ± √(b² - 4ac)) / (2a).

Front

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

Back

To solve a quadratic equation using the quadratic formula, identify the coefficients a, b, and c from the equation, substitute them into the formula, and simplify to find the values of x.

Front

What are the roots of the equation 15x² + 22x + 8 = 0?

Back

The roots of the equation can be found using the quadratic formula, yielding x = -2/3 and x = -4/5.

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What does it mean for a number to be a factor of a polynomial?

Back

A number is a factor of a polynomial if, when the polynomial is divided by that number, the remainder is zero.

Front

How do you find the increasing interval of a quadratic function?

Back

To find the increasing interval of a quadratic function, determine the vertex and analyze the direction of the parabola. The function increases to the right of the vertex.

Front

What is the vertex of the function f(x) = 3x² - 9?

Back

The vertex of the function f(x) = 3x² - 9 is at the point (0, -9).

Front

What is the end behavior of a quadratic function as x approaches infinity?

Back

For a quadratic function in the form ax² + bx + c, if a > 0, the end behavior as x approaches infinity is +∞; if a < 0, it is -∞.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots of a quadratic equation: if positive, there are two distinct real roots; if zero, one real root; if negative, two complex roots.

Front

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

Back

To determine the x-intercepts of a quadratic function, set the function equal to zero and solve for x using factoring, the quadratic formula, or completing the square.