Algebra 2 Midterm Review

Front

What is the solution to the equation f(x) = g(x) where f(x) = -0.15x^3 - x^2 - x - 3.2 and g(x) = 1.2|x + 6| + 2.4?

Back

The solution is x = -6.6.

Front

If the graph of a function bounces right off the x-axis, what does that indicate about the multiplicity of that factor?

Back

The multiplicity of that factor is 2.

Front

Factor the expression 27x³ - 64.

Back

The factored form is (3x - 4)(9x² + 12x + 16).

Front

Describe the end behavior of the graph of a polynomial function where x → ∞, y → ∞ and x → -∞, y → 0.

Back

As x approaches infinity, y approaches infinity; as x approaches negative infinity, y approaches 0.

Front

Is the leading coefficient of the polynomial function positive or negative if it is given that the leading term is -0.15x^3?

Back

The leading coefficient is negative.

Front

What does it mean if a polynomial function has a factor with an odd multiplicity?

Back

It means the graph will cross the x-axis at that root.

Front

What is the end behavior of a polynomial function with a positive leading coefficient and an even degree?

Back

As x → ∞, y → ∞ and as x → -∞, y → ∞.

Front

How do you determine the number of real roots of a polynomial function?

Back

By analyzing the degree of the polynomial and its factors.

Front

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

Back

The vertex represents the maximum or minimum point of the parabola.

Front

What is the quadratic formula used for?

Back

To find the solutions (roots) of a quadratic equation in the form ax^2 + bx + c = 0.