Solving Quadratics and Quadratic Formula

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 is the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation and is given by x = (-b ± √(b² - 4ac)) / (2a).

Tags

CCSS.HSA-REI.B.4B

Front

What does the discriminant (b² - 4ac) tell us?

Back

The discriminant indicates the nature of the roots of a quadratic equation: if it's 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 convert a quadratic equation to standard form?

Back

To convert a quadratic equation to standard form, rearrange it to the form ax² + bx + c = 0 by moving all terms to one side.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph of a quadratic function, depending on whether it opens upwards or downwards.

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex (h, k) can be found using the formula h = -b/(2a) and k = f(h), where f(x) is the quadratic function.

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 is factoring in relation to quadratic equations?

Back

Factoring is the process of expressing a quadratic equation as a product of two binomials, which can help in finding the roots.

Tags

CCSS.HSA-REI.B.4B

Front

What is the zero product property?

Back

The zero product property states that if the product of two factors is zero, then at least one of the factors must be zero.

Tags

CCSS.HSA-REI.B.4B

Front

How do you solve a quadratic equation by factoring?

Back

To solve by factoring, set the equation to zero, factor it into two binomials, and then set each factor equal to zero to find the solutions.

Tags

CCSS.HSA-REI.B.4B