Quadratic Formula and Discriminant

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is used to find the solutions of a quadratic equation in the form ax² + bx + c = 0. It is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

What does the Discriminant tell us?

Back

The Discriminant (D = b² - 4ac) determines the nature of the roots of a quadratic equation. If D > 0, there are 2 real solutions; D = 0, there is 1 real solution; D < 0, there are no real solutions.

Front

Solve using the Quadratic Formula: 2x² + 2x - 12 = 0

Back

x = 2, -3

Front

What are the solutions of the graph of a quadratic equation?

Back

The solutions (or roots) of the graph are the x-values where the graph intersects the x-axis.

Front

If a quadratic graph does not intercept the x-axis, how many real solutions does it have?

Back

No Real Solution.

Front

Use the Discriminant to determine the number of solutions for: -2x² - x - 1 = 0

Back

D = (-1)² - 4(-2)(-1) = 1 - 8 = -7; No Solutions.

Front

Identify a, b, and c in the equation: 4x² - 8x = 3

Back

a = 4, b = -8, c = -3.

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.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point on the graph of a quadratic function, given by the coordinates (h, k) where h = -b/(2a) and k is the function value 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 images, given by the equation x = -b/(2a).