Solving Quadratics - All Methods

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, 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

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 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 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.

Tags

CCSS.HSA-REI.B.4B

Front

What is the vertex form of a quadratic equation?

Back

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

Front

How can you determine the vertex of a quadratic function?

Back

The vertex can be found using the formula h = -b/(2a) for the x-coordinate, and then substituting h back into the equation to find the y-coordinate.

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

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph of the quadratic function crosses the x-axis, found by solving the equation ax² + bx + c = 0.

Tags

CCSS.HSF-IF.C.7A