Quadratic Functions Flashcard-12/13

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which opens upwards if a > 0 and downwards if a < 0.

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

How do you find the axis of symmetry for a quadratic function?

Back

The axis of symmetry can be found using the formula x = -b/(2a), where a and b are coefficients from the quadratic equation.

Front

What are the roots of a quadratic equation?

Back

The roots (or x-intercepts) are the values of x where the graph intersects the x-axis, found by solving the equation ax² + bx + c = 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

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

Back

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

Front

What is the formula for the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula (h, k) where h = -b/(2a) and k = f(h).

Front

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

Back

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

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.