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 profit from a quadratic profit function?

Back

To find the maximum profit from a quadratic function P = ax² + bx + c, use the formula s = -b/(2a) to find the selling price that maximizes profit.

Front

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

Back

The 'a' value indicates the direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

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, which occurs when x = 0. It represents the value of the function at that point.

Front

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

Back

To find the x-intercepts, set the quadratic equation to zero and solve for x using factoring, completing the square, or the quadratic formula.

Front

What is the quadratic formula?

Back

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

Front

What is the difference between a function with a maximum value and one with a minimum value?

Back

A function with a maximum value has a peak point (vertex) and opens downwards, while a function with a minimum value has a trough point and opens upwards.

Front

What are the characteristics of a parabola?

Back

A parabola is symmetric about its vertex, can open upwards or downwards, and has a specific vertex, axis of symmetry, and intercepts.

Front

How can you tell if a quadratic function will have real solutions?

Back

You can determine if a quadratic function has real solutions by evaluating the discriminant (b² - 4ac): if it's positive, there are two real solutions; if zero, one real solution; if negative, no real solutions.

Front

What is an inequality in the context of quadratic functions?

Back

An inequality involving a quadratic function expresses a relationship where the function is greater than or less than a certain value, often resulting in a range of x-values.