Quadratic Functions and Equations

Front

Distribute and simplify the expression: (x - 3i)(x + 3i)

Back

x^2 - 9

Front

Distribute and simplify the expression: (4 + i)(5 - 2i)

Back

22 - 3i

Front

Factor the expression: 3x^2 - 60x + 300

Back

3(x - 10)^2

Front

Factor the expression: x^2 + 16x - 36

Back

(x + 18)(x - 2)

Front

Find the solutions to the equation: -5(6x - 4)(x - 2) = 0

Back

x = 2/3 and x = 2

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola represented by the quadratic function, found at the point (h, k) in the vertex form f(x) = a(x - h)^2 + k.

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-image halves, given by the equation x = -b/(2a) for the standard form f(x) = ax^2 + bx + c.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation and is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

What does the discriminant tell us about a quadratic equation?

Back

The discriminant (D = b² - 4ac) indicates the nature of the roots: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are two complex roots.