IM2 Fall 2024 Semester Exam Review

Front

Is this a perfect square trinomial? x^2 + 14x + 49

Back

Yes, it is a perfect square trinomial because it can be factored as (x + 7)(x + 7) or (x + 7)^2.

Front

Factor completely: k^2 - 2k - 24

Back

(k + 4)(k - 6)

Front

In the vertex form f(x) = a(x - h)² + k, what does the 'k' value do?

Back

The 'k' value shifts the function up or down.

Front

What value of c would make this a perfect square trinomial? x^2 + 2x + c

Back

c = 1, because (x + 1)^2 = x^2 + 2x + 1.

Front

Multiply: (2x - 7)(x + 2)

Back

2x^2 - 3x - 14.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be expressed as the square of a binomial, such as (a + b)^2 = a^2 + 2ab + b^2.

Front

How do you identify a perfect square trinomial?

Back

A trinomial is a perfect square if the first and last terms are perfect squares and the middle term is twice the product of the square roots of the first and last terms.

Front

What is the vertex form of a quadratic function?

Back

The vertex form is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

What does the 'a' value in vertex form indicate?

Back

The 'a' value indicates the direction of the parabola (upward if a > 0, downward if a < 0) and its vertical stretch or compression.

Front

What is the process to factor a quadratic expression?

Back

To factor a quadratic expression, find two numbers that multiply to the constant term and add to the coefficient of the linear term.