IA Review Part 1 Quadratics

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

Identify the standard form of a quadratic equation.

Back

The standard form of a quadratic equation is y = ax² + bx + c.

Front

What does the term 'discriminant' refer to in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac, which determines the nature of the roots.

Front

How do you find the values of a, b, and c in the equation 4x² - 8x = 3?

Back

Rearrange to standard form: 4x² - 8x - 3 = 0. Here, a = 4, b = -8, c = -3.

Front

What is the value of the discriminant for the equation y = 2x² - x - 3?

Back

The discriminant is calculated as b² - 4ac = (-1)² - 4(2)(-3) = 1 + 24 = 25.

Front

Solve for b: 5b² - 4 = 41.

Back

5b² = 45; b² = 9; b = ±3.

Front

What are the possible values of b in the equation 9k² = 225?

Back

k² = 25; k = ±5.

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 negative discriminant indicate about the roots of a quadratic equation?

Back

A negative discriminant indicates that the quadratic equation has no real roots, only complex 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 (a repeated root).