Solving Quadratic Equations

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in 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, using the quadratic formula, completing the square, and graphing.

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.

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.

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 the vertex of a parabola represented by a quadratic equation?

Back

The vertex of a parabola is the highest or lowest point on the graph, found at the coordinates (h, k), where h = -b/(2a) and k is the value of the quadratic function at h.

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).

Front

How do you complete the square for a quadratic equation?

Back

To complete the square, rearrange the equation to isolate the constant term, then add and subtract (b/2)² to form a perfect square trinomial.

Front

What is the significance of the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero, representing the x-intercepts of the graph.

Front

How do you round answers to the nearest hundredth?

Back

To round to the nearest hundredth, look at the third decimal place: if it's 5 or greater, round up the second decimal place by one; if it's less than 5, keep the second decimal place the same.