Solving Quadratics

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

Front

What does the discriminant of a quadratic equation indicate?

Back

The discriminant (D = b² - 4ac) indicates the nature of the roots of the quadratic equation: D > 0 means two distinct real roots, D = 0 means one real root, and D < 0 means no real roots.

Front

How do you calculate the discriminant for the equation 5x² + x - 2 = 0?

Back

D = b² - 4ac = (1)² - 4(5)(-2) = 1 + 40 = 41.

Front

What is the zero product property?

Back

The zero product property states that if the product of two factors is zero, then at least one of the factors must be zero.

Front

Solve the equation: (x - 9)(x + 3) = 0

Back

x = 9 or x = -3.

Front

What are the roots of the equation 4m² - 100 = 0?

Back

m = 5 or m = -5.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation 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 (h, k) can be found using h = -b/(2a) and k = f(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).