EM2 - Unit 2 Retake Flashcardizz (updated)

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the value calculated from the coefficients of a quadratic equation in the form ax² + bx + c, given by the formula b² - 4ac. It determines the nature of the roots of the equation.

Front

What does a positive discriminant indicate about the roots of a quadratic equation?

Back

A positive discriminant indicates that the quadratic equation has two distinct real roots.

Front

What does a discriminant of zero indicate about the roots of a quadratic equation?

Back

A discriminant of zero indicates that the quadratic equation has exactly one real root, also known as a repeated or double root.

Front

What does a negative discriminant indicate about the roots of a quadratic equation?

Back

A negative discriminant indicates that the quadratic equation has two complex (imaginary) roots.

Front

How do you solve a quadratic equation by factoring?

Back

To solve a quadratic equation by factoring, express the equation in the form ax² + bx + c = 0, factor it into the form (px + q)(rx + s) = 0, and then set each factor equal to zero to find the solutions.

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

What is the vertex of a parabola?

Back

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

Front

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

Back

The vertex (h, k) of a quadratic function in standard form y = ax² + bx + c can be found using the formula h = -b/(2a) and k = f(h).

Front

What is the axis of symmetry in a parabola?

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 the maximum height of a projectile?

Back

The maximum height of a projectile can be found using the vertex of the quadratic function that models its height over time.