Domain, Range, and Key Features of Quadratics

Front

What is the definition of the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the definition of the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

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.

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 are the key features of a quadratic function?

Back

Key features include the vertex, axis of symmetry, y-intercept, x-intercepts (zeros), and the direction of the parabola (opening up or down).

Front

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

Back

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

Front

What are x-intercepts of a quadratic function?

Back

X-intercepts are the points where the graph of the function crosses the x-axis, also known as the zeros of the function.

Front

How can you determine the number of zeros of a quadratic function?

Back

The number of zeros can be determined using the discriminant (b² - 4ac) from the quadratic formula. If the discriminant is positive, there are 2 zeros; if it is zero, there is 1 zero; if negative, there are no real zeros.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens upwards or downwards.

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).