Quadratic Formula

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

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

Back

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

Front

Can the quadratic formula be used to solve quadratic equations that cannot be factored?

Back

Yes, the quadratic formula can be used to solve quadratic equations that cannot be factored.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is given by the formula b² - 4ac.

Front

In the quadratic equation ax² + bx + c = 0, what does the c term represent?

Back

The c term represents the constant term in the equation.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a).

Front

What does the discriminant tell us about the roots of a quadratic equation?

Back

The discriminant indicates the nature of the roots: if > 0, two distinct real roots; if = 0, one real root; if < 0, no real roots.

Front

How do you convert the equation 4x² - 8x = 3 into standard form?

Back

Subtract 3 from both sides to get 4x² - 8x - 3 = 0.

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

What is the axis of symmetry in a quadratic equation?

Back

The axis of symmetry is the vertical line x = -b/(2a).