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 y = ax² + bx + c.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.

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 formula x = -b/(2a).

Front

What are the roots of a quadratic equation?

Back

The roots (or x-intercepts) are the values of x that make the equation equal to zero.

Front

How do you find the y-intercept of a quadratic function?

Back

The y-intercept is found by evaluating the function at x = 0.

Front

What is the quadratic formula?

Back

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

Front

What does the discriminant tell us about a quadratic equation?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.

Front

What is a parabola?

Back

A parabola is the graph of a quadratic function, which is U-shaped and can open upwards or downwards.

Front

What are the factors of the quadratic equation x² + 5x + 6 = 0?

Back

The factors are (x + 2)(x + 3), and the solutions are x = -2 and x = -3.