Characteristics of Quadratic Equations

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form f(x) = ax² + bx + c, 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 f(x) = ax² + bx + c.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

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

Back

To find the y-intercept, set x = 0 in the equation and solve for f(0).

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 formula x = -b/(2a).

Front

What are the zeros of a quadratic function?

Back

The zeros (or roots) are the values of x for which f(x) = 0, representing the points where the graph intersects the x-axis.

Front

How can you determine the number of real roots of a quadratic equation?

Back

The number of real roots can be determined using the discriminant, D = b² - 4ac. If D > 0, there are 2 real roots; D = 0, 1 real root; D < 0, no real roots.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on the direction it opens. It can be found using the vertex form or by calculating (-b/(2a), f(-b/(2a))).

Front

What does it mean for a quadratic function to open upwards or downwards?

Back

A quadratic function opens upwards if a > 0 and downwards if a < 0.

Front

What is the significance of the coefficient 'a' in a quadratic equation?

Back

The coefficient 'a' determines the direction of the parabola (upward or downward) and affects the width of the parabola.