Alg 2 - 1st Semester Review 2024 Pt 2

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, represented as (h, k) in the vertex form y = a(x - h)² + k.

Front

How do you factor by grouping?

Back

To factor by grouping, group terms with common factors, factor them out, and then factor the resulting expression.

Front

What is the solution to a system of equations?

Back

The solution is the point where the graphs of the equations intersect, representing the values of the variables that satisfy all equations.

Front

How do you evaluate a function at a specific point?

Back

To evaluate f(x) at x = a, substitute a into the function and simplify.

Front

What does shifting a graph up or down mean?

Back

Shifting a graph up means adding a constant to the function, while shifting down means subtracting a constant.

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax² + bx + c = 0, where a, b, and c are constants.

Front

What is the quadratic formula?

Back

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

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by x = -b/(2a).

Front

What does it mean for a quadratic to open upwards or downwards?

Back

A quadratic opens upwards if a > 0 and downwards if a < 0 in the standard form ax² + bx + c.

Front

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

Back

The discriminant (b² - 4ac) determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.