Solving Quadratics

Front

What are the values of a, b, and c in the quadratic equation 4x² - 8x = 3?

Back

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

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax² + bx + c.

Front

What is the degree of a quadratic equation?

Back

The degree of every quadratic equation is 2.

Front

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

Back

Rearrange to 4x² - 8x - 3 = 0.

Front

What is the quadratic formula used for?

Back

The quadratic formula is used to find the roots of a quadratic equation.

Front

What is the quadratic formula?

Back

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

Front

What does the discriminant (b² - 4ac) tell us about a quadratic equation?

Back

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

Front

What does it mean to solve a quadratic equation by factoring?

Back

It means to express the quadratic equation as a product of its linear factors and then set each factor to zero.

Front

What are the roots of the quadratic equation 4x² - 8x - 3 = 0?

Back

The roots are x = -2 and x = 4.

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.