4.5 Completing the Square

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, allowing for easier solving of the equation.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants.

Front

How do you find the value of 'c' to complete the square for the expression x^2 + 8x + c?

Back

To complete the square, take half of the coefficient of x (which is 8), square it (4^2 = 16), so c = 16.

Front

What is a perfect square trinomial?

Back

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

Front

Solve the equation by completing the square: x^2 + 4x + 1 = 0.

Back

x = -2 ± √3.

Front

Solve the equation by completing the square: x^2 + 12x + 8 = 0.

Back

x = -6 ± 2√7.

Front

Find the missing value 'c' to create a perfect square trinomial: x^2 + 26x + ___.

Back

c = 169.

Front

What is the vertex form of a quadratic equation?

Back

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

Front

How do you derive the quadratic formula from completing the square?

Back

By completing the square on the standard form ax^2 + bx + c = 0, you derive the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a).

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.