Algebra EOC RC 4

Front

What is the domain of a quadratic function representing a real-world scenario?

Back

The domain of a quadratic function is the set of all possible input values (x-values) for which the function is defined. In real-world scenarios, it often represents the range of values that make sense in context.

Front

How do you find the solutions to a quadratic equation in the form ax^2 + bx + c = 0?

Back

You can find the solutions using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a). Alternatively, you can factor the equation if possible.

Front

What are the zeros of a quadratic function?

Back

The zeros of a quadratic function are the x-values where the function equals zero. They can be found by solving the equation f(x) = 0.

Front

What does the vertex of a quadratic function represent?

Back

The vertex of a quadratic function represents the highest or lowest point on the graph, depending on whether the parabola opens upwards or downwards.

Front

How can you determine if a quadratic function opens upwards or downwards?

Back

A quadratic function opens upwards if the coefficient of x² (a) is positive and downwards if a is negative.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (D = b² - 4ac) determines 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 no real roots.

Front

How do you convert a quadratic function from vertex form to standard form?

Back

To convert from vertex form (y = a(x - h)² + k) to standard form (y = ax² + bx + c), expand the squared term and simplify.

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. It can be found using the formula x = -b/(2a).

Front

How do you model real-world data with a quadratic function?

Back

To model real-world data, collect data points, plot them, and use regression analysis to find a quadratic function that best fits the data.