Solving Quadratic Equations (All Methods + Complex Solutions)

Front

What is a quadratic equation?

Back

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

Front

What are the methods to solve quadratic equations?

Back

The methods to solve quadratic equations include factoring, completing the square, using the quadratic formula, and graphing.

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 solutions of a quadratic equation.

Tags

CCSS.HSA-REI.B.4B

Front

What does the discriminant of a quadratic equation indicate?

Back

The discriminant, given by b² - 4ac, indicates the nature of the roots: if positive, there are two distinct real roots; if zero, there is one real root; if negative, there are two complex roots.

Tags

CCSS.HSA-REI.B.4B

Front

How do you factor a quadratic equation?

Back

To factor a quadratic equation, find two numbers that multiply to ac (the product of a and c) and add to b (the coefficient of x). Then, rewrite the equation in factored form.

Front

What is completing the square?

Back

Completing the square is a method used to solve quadratic equations by rewriting the equation in the form (x - p)² = q, making it easier to solve for x.

Tags

CCSS.HSA-REI.B.4B

Front

What are complex solutions in quadratic equations?

Back

Complex solutions occur when the discriminant is negative, resulting in solutions that include imaginary numbers, expressed in the form a + bi.

Tags

CCSS.HSA-REI.B.4B

CCSS.HSN.CN.C.7

Front

How can you graph a quadratic equation?

Back

To graph a quadratic equation, plot the vertex, axis of symmetry, and intercepts, then draw a parabola opening upwards or downwards based on the sign of a.

Tags

CCSS.HSF-IF.C.7A

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, found using the formula (-b/(2a), f(-b/(2a))).

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a).