Algebra 2 - Final Review

Front

What is the vertex form of a quadratic function?

Back

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

Front

How do you find the maximum or minimum value of a quadratic function?

Back

To find the maximum or minimum value of a quadratic function in the form y = ax² + bx + c, use the formula x = -b/(2a) to find the x-coordinate of the vertex, then substitute this value back into the function.

Front

What does the 'a' value in a quadratic function indicate about the graph?

Back

The 'a' value determines the direction of the parabola: if 'a' is positive, the parabola opens upwards (minimum point); if 'a' is negative, it opens downwards (maximum point).

Front

What is the standard form of a quadratic equation?

Back

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

Front

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

Back

The discriminant is given by D = b² - 4ac. It indicates the nature of the roots: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Front

How do you solve a quadratic equation using factoring?

Back

To solve a quadratic equation by factoring, express it in the form (x - p)(x - q) = 0, where p and q are the roots, then set each factor to zero: x - p = 0 and x - q = 0.

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 the equation x = -b/(2a).

Front

What is the significance of the y-intercept in a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, found by evaluating the function at x = 0, which gives the value of c in the standard form y = ax² + bx + c.

Front

How can you determine the intervals where a quadratic function is increasing or decreasing?

Back

To determine the intervals of increase or decrease, find the vertex using x = -b/(2a). The function is increasing to the right of the vertex and decreasing to the left.

Front

What is a quadratic inequality?

Back

A quadratic inequality is an inequality that involves a quadratic expression, such as ax² + bx + c < 0 or ax² + bx + c ≥ 0, and can be solved to find the range of x values.