Quadratic Formula

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 (b² - 4ac) indicate?

Back

The discriminant indicates the nature of the roots of a quadratic equation. If it is positive, there are 2 real solutions; if it is zero, there is 1 real solution; if it is negative, there are no real solutions.

Front

If the discriminant is negative, how many real solutions does the quadratic have?

Back

No real solution.

Front

Identify the values of a, b, and c in the equation: 4x² – 8x – 3 = 0.

Back

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

Front

What is the value of 'a' in the equation y = x² - 8x - 24?

Back

1.

Front

What is the value of 'b' in the equation y = 16x² - 8x - 24?

Back

-8.

Front

What is the value of 'c' in the equation y = 16x² - 8x - 24?

Back

-24.

Front

What is the vertex form of a quadratic equation?

Back

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

Front

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

Back

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