IM2 Fall 2024 Semester Exam

Front

What is the axis of symmetry for a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror images. It can be found using the formula x = -b/(2a) for a quadratic in the form y = ax^2 + bx + c.

Front

How do you write the equation of a quadratic function in vertex form?

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

What is the formula to find the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value of a quadratic function y = ax^2 + bx + c occurs at x = -b/(2a). Substitute this x-value back into the function to find the corresponding y-value.

Front

How do you complete the square for the expression x^2 + 6x?

Back

To complete the square, take half of the coefficient of x (which is 6), square it (3^2 = 9), and add it to the expression: x^2 + 6x + 9 = (x + 3)^2.

Front

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

Back

The vertex represents the highest or lowest point of the parabola, depending on whether it opens upwards or downwards.

Front

How do you determine the direction of a parabola?

Back

The direction of a parabola is determined by the coefficient 'a' in the quadratic equation y = ax^2 + bx + c. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the roots 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: if it's positive, there are two distinct real roots; if zero, there is one real root; if negative, there are no real roots.

Front

How can you find the maximum height of a projectile modeled by a quadratic function?

Back

The maximum height can be found by determining the vertex of the quadratic function that models the projectile's height over time.

Front

What is the standard form of a quadratic function?

Back

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