Solving quadratic Equations by completing the Squares

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 (x - p)² = q, where p and q are constants. This method allows for easier solving of the equation.

Tags

CCSS.HSA-REI.B.4B

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

How do you find the value of C when completing the square for the expression x² + bx + C?

Back

To find C, take half of the coefficient of x (which is b), square it, and add it to the expression. C = (b/2)².

Tags

CCSS.HSA-REI.B.4B

Front

What are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that satisfy the equation, which can be found using methods such as factoring, completing the square, or the quadratic formula.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

Front

How do you solve the equation n² - 2n - 3 = 0 by completing the square?

Back

To solve by completing the square, rewrite the equation as (n - 1)² - 4 = 0, then solve for n to find n = 3 and n = -1.

Tags

CCSS.HSA-REI.B.4B

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if positive, there are two distinct real roots; if zero, one real root; if negative, two complex roots.

Tags

CCSS.HSA-REI.B.4B

Front

How can you express a quadratic equation in vertex form?

Back

A quadratic equation can be expressed in vertex form as y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

What does it mean for a quadratic equation to have complex roots?

Back

Complex roots occur when the discriminant is negative, resulting in roots that are not real numbers and can be expressed in the form a ± bi.

Tags

CCSS.HSN.CN.A.3

Front

How do you solve y² + 10y = -9 by completing the square?

Back

Rearrange to y² + 10y + 25 = 16, then factor to (y + 5)² = 16, leading to y = -5 ± 4, giving roots y = -1 and y = -9.

Tags

CCSS.HSA-REI.B.4B