MATH 2 - FINAL EXAM REVIEW

Front

Find the axis of symmetry for the function f(x)= x² + 2x + 6

Back

The axis of symmetry for a quadratic function in the form f(x) = ax² + bx + c is given by the formula x = -b/(2a). For f(x) = x² + 2x + 6, a = 1 and b = 2, so the axis of symmetry is x = -2/(2*1) = -1.

Front

Factor the expression x² + 11x + 24

Back

To factor the quadratic expression x² + 11x + 24, we look for two numbers that multiply to 24 and add to 11. The factors are 8 and 3, so the expression can be factored as (x + 8)(x + 3).

Front

Find the roots of the following function 2x² + 2x - 12

Back

To find the roots of the quadratic equation 2x² + 2x - 12, we can use the quadratic formula x = (-b ± √(b² - 4ac)) / (2a). Here, a = 2, b = 2, and c = -12. The roots are x = 2 and x = -3.

Front

Which of the following represents inverse variation?

Back

Inverse variation is represented by the equation y = k/x, where k is a constant. This means that as one variable increases, the other decreases.

Front

Reflect the point (2, -4) over the y-axis.

Back

To reflect a point over the y-axis, you change the sign of the x-coordinate. The reflection of (2, -4) is (-2, -4).

Front

What is the vertex of the parabola represented by f(x) = x² + 2x + 6?

Back

The vertex of a parabola in the form f(x) = ax² + bx + c can be found using the formula (-b/(2a), f(-b/(2a))). For f(x) = x² + 2x + 6, the vertex is (-1, 5).

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 ax² + bx + c = 0.

Front

What does it mean for two expressions to be equivalent?

Back

Two expressions are equivalent if they have the same value for all values of the variable(s) involved.

Front

How do you complete the square for the expression x² + 6x?

Back

To complete the square for x² + 6x, take half of the coefficient of x (which is 3), square it (9), and rewrite the expression as (x + 3)² - 9.

Front

What is the discriminant of a quadratic equation?

Back

The discriminant of a quadratic equation ax² + bx + c is given by D = b² - 4ac. It determines 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.