Unit 4B Flashcard Review

Front

What is the process of completing the square in a quadratic equation?

Back

Completing the square involves rewriting a quadratic equation in the form of (x + p)^2 = q, where p and q are constants. This helps in solving the equation and understanding its graph.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be factored into the square of a binomial, such as (x + a)^2 = x^2 + 2ax + a^2.

Front

How do you find the value of 'c' to create a perfect square trinomial from x^2 - 8x + ___?

Back

To find 'c', take half of the coefficient of x (-8), square it: (-4)^2 = 16. Thus, c = 16.

Front

What is the Square Root method for solving quadratic equations?

Back

The Square Root method involves isolating the x^2 term and taking the square root of both sides to find the values of x.

Front

Solve by the Square Root method: x^2 = 16. What are the solutions?

Back

The solutions are ±4, since taking the square root of both sides gives x = ±√16.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the roots of a quadratic equation in the form ax^2 + bx + c = 0, given by x = (-b ± √(b^2 - 4ac)) / (2a).

Front

How do you apply the quadratic formula to the equation x^2 + 9x + 9 = 0?

Back

Identify a = 1, b = 9, c = 9. Substitute into the formula: x = (-9 ± √(9^2 - 4*1*9)) / (2*1) = (-9 ± √45) / 2.

Front

What does the discriminant of a quadratic equation tell you?

Back

The discriminant (b^2 - 4ac) indicates the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.

Front

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

Back

The vertex represents the maximum or minimum point of the parabola described by the quadratic function, indicating the highest or lowest value of the function.

Front

How can you determine the axis of symmetry for a quadratic function?

Back

The axis of symmetry can be found using the formula x = -b/(2a) from the quadratic equation ax^2 + bx + c.